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Algebraic structure
mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra
Commutative_ring
Algebraic structure with addition and multiplication
addition and multiplication, except that multiplication in a ring does not need to be commutative. Ring elements may be numbers such as integers or complex numbers
Ring_(mathematics)
Algebraic structure
commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group rings,
Polynomial_ring
Vector space equipped with a bilinear product
associative commutative algebra. Replacing the field of scalars by a commutative ring leads to the more general notion of an algebra over a ring. Algebras
Algebra_over_a_field
Branch of algebra that studies commutative rings
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both
Commutative_algebra
Algebraic structure
mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different
Noncommutative_ring
Branch of algebra
examples of commutative rings, have driven much of the development of commutative ring theory, which is now, under the name of commutative algebra, a major
Ring_theory
Mathematical ring with well-behaved ideals
right-Noetherian. Noetherian rings are fundamental in both commutative and noncommutative ring theory since many rings that are encountered in mathematics
Noetherian_ring
Ring that is also a vector space or a module
mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A
Associative_algebra
Submodule of a mathematical ring
beyond number rings to the setting of polynomial rings and other commutative rings by David Hilbert and especially Emmy Noether. Given a ring R {\displaystyle
Ideal_(ring_theory)
In algebra, a graded-commutative ring (also called a skew-commutative ring) is a graded ring that is commutative in the graded sense; that is, homogeneous
Graded-commutative_ring
Generalization of vector spaces from fields to rings
space in which the field of scalars is replaced by a (not necessarily commutative) ring. The concept of a module also generalizes the notion of an abelian
Module_(mathematics)
Algebraic structure also called skew field
a b–1 ≠ b–1 a. A commutative division ring is a field. Wedderburn's little theorem asserts that all finite division rings are commutative and therefore finite
Division_ring
(Mathematical) ring with a unique maximal ideal
is the branch of commutative algebra that studies commutative local rings and their modules. In practice, a commutative local ring often arises as the
Local_ring
Ideal in a ring which has properties similar to prime elements
and prime ideals are both primary and semiprime. An ideal P of a commutative ring R is prime if it has the following two properties: If a and b are two
Prime_ideal
In mathematics, invariant of square matrices
entries in a non-commutative ring, there are various difficulties in defining determinants analogously to that for commutative rings. A meaning can be
Determinant
Construction of a ring of fractions
In commutative algebra and algebraic geometry, localization is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces
Localization (commutative algebra)
Localization_(commutative_algebra)
Branch of mathematics
studies the geometric properties of formal duals of non-commutative algebraic objects such as rings as well as geometric objects derived from them (e.g.
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Structure-preserving function between two rings
over a commutative ring R is a ring homomorphism that is also R-linear. The function f : Z/6Z → Z/6Z defined by f([a]6) = [4a]6 is not a ring homomorphism
Ring_homomorphism
Property of some mathematical operations
whose operation is commutative; a commutative ring is a ring whose multiplication is commutative. (Addition in a ring is always commutative.) However, in the
Commutative_property
Category whose objects are rings and whose morphisms are ring homomorphisms
Ring is a commutative ring. The action of a monoid (= commutative ring) R on an object (= ring) A of Ring is an R-algebra. The category of rings has a number
Category_of_rings
Mathematical operation on vector spaces
adjoint" to Hom. The tensor product of two modules A and B over a commutative ring R is defined in exactly the same way as the tensor product of vector
Tensor_product
Sheaf of rings in mathematics
mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that
Ringed_space
Ideal of the nilpotent elements
In algebra, the nilradical of a commutative ring is the ideal consisting of the nilpotent elements: N R = N i l ( R ) = { f ∈ R ∣ f m = 0 for some m
Nilradical_of_a_ring
Set of a ring's prime ideals
more specifically in commutative algebra and algebraic geometry, the prime spectrum (or simply the spectrum) of a commutative ring R {\displaystyle R}
Spectrum_of_a_ring
In mathematics, element with a multiplicative inverse
nonzero ring R in which every nonzero element is a unit (that is, R× = R ∖ {0}) is called a division ring (or a skew-field). A commutative division ring is
Unit_(ring_theory)
Algebra over a field where binary multiplication is not necessarily associative
associative", just as "noncommutative" means "not necessarily commutative" for noncommutative rings. An algebra is unital or unitary if it has an identity element
Non-associative_algebra
Set with operations obeying given axioms
algebraic structure that is a vector space over a field or a module over a commutative ring. The collection of all structures of a given type (same operations
Algebraic_structure
Commutative monoid in simplicial abelian groups
In algebra, a simplicial commutative ring is a commutative monoid in the category of simplicial abelian groups, or, equivalently, a simplicial object
Simplicial_commutative_ring
algebraic topology, a commutative ring spectrum, roughly equivalent to a E ∞ {\displaystyle E_{\infty }} -ring spectrum, is a commutative monoid in a good
Commutative_ring_spectrum
Type of algebraic structure
-graded ring. If I is an ideal in a commutative ring R, then ⨁ n = 0 ∞ I n / I n + 1 {\textstyle \bigoplus _{n=0}^{\infty }I^{n}/I^{n+1}} is a graded ring called
Graded_ring
Generalization of algebraic variety
variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers). Scheme
Scheme_(mathematics)
Free object in the category of associative algebras
variables. Likewise, the polynomial ring may be regarded as a free commutative algebra. For R a commutative ring, the free (associative, unital) algebra
Free_algebra
Type of ring in commutative algebra
In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal
Regular_local_ring
Direct summand of a free module (mathematics)
left R-modules and Ab is the category of abelian groups. When the ring R is commutative, Ab is advantageously replaced by R-Mod in the preceding characterization
Projective_module
Commutative group (mathematics)
In mathematics, an abelian group,[note 1] also called a commutative group, is a group in which the result of applying the group operation to two group
Abelian_group
Algebraic structure in ring theory
a right exact functor.) These definitions apply also if R is a non-commutative ring, and M is a left R-module; in this case, K, L and J must be right R-modules
Flat_module
Algebraic structure with addition, multiplication, and division
multiplication distributes over addition. Even more succinctly: a field is a commutative ring in which 0 ≠ 1 and all nonzero elements are invertible under multiplication
Field_(mathematics)
In algebra, module with a finite generating set
polynomial ring R[X] over a Noetherian ring R is Noetherian. Both facts imply that a finitely generated commutative algebra over a Noetherian ring is again
Finitely_generated_module
Algebraic ring that need not have additive negative elements
definition, any ring and any semifield is also a semiring. The non-negative elements of a commutative, discretely ordered ring form a commutative, discretely
Semiring
Commutative ring with no zero divisors other than zero
In mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. In an integral domain, every
Integral_domain
In mathematics, dimension of a ring
In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime
Krull_dimension
Operation that pairs a left and a right R-module into an abelian group
of modules over a commutative ring resulting in a third module, and also for a pair of a right-module and a left-module over any ring, with result an abelian
Tensor_product_of_modules
Concept in mathematics
and algebraic topology. A one-dimensional formal group law over a commutative ring R is a (formal) power series F(x,y) with coefficients in R, such that
Formal_group_law
German mathematician (1882–1935)
in Ringbereichen (Theory of Ideals in Ring Domains), Noether developed the theory of ideals in commutative rings into a tool with wide-ranging applications
Emmy_Noether
Local ring in commutative algebra
In commutative algebra, a Gorenstein local ring is a commutative Noetherian local ring R with finite injective dimension as an R-module. There are many
Gorenstein_ring
Mathematical structure in abstract algebra
is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R
*-algebra
Unique ring consisting of one element
zero ring is commutative. The element 0 in the zero ring is a unit, serving as its own multiplicative inverse. The unit group of the zero ring is the
Zero_ring
Generalization of associativity properties
modules over a commutative ring, chain complexes, groupoids (or even the category of categories itself), coalgebras, etc. Given a commutative ring R we consider
Operad
subject. For the items in commutative algebra (the theory of commutative rings), see Glossary of commutative algebra. For ring-theoretic concepts in the
Glossary_of_ring_theory
Largest integer that divides given integers
(see Polynomial greatest common divisor) and other commutative rings (see § In commutative rings below). The greatest common divisor (GCD) of integers
Greatest_common_divisor
Branch of mathematics
denoted as 1. Multiplication needs not to be commutative; if it is commutative, one has a commutative ring. The ring of integers ( Z {\displaystyle \mathbb
Algebra
Graph of zero divisors of a commutative ring
combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has elements of the ring as
Zero-divisor_graph
Class of mathematical expression
inverses to a commutative ring is called localization. However, the localization of every commutative ring at zero is the trivial ring, where 0 = 1
Division_by_zero
Topology on prime ideals and algebraic varieties
generalized for making the set of prime ideals of a commutative ring (called the spectrum of the ring) a topological space. The Zariski topology allows
Zariski_topology
Reduction of a ring by one of its ideals
associative algebra A {\displaystyle A} over a commutative ring R {\displaystyle R} is itself a ring. If I {\displaystyle I} is an ideal in A {\displaystyle
Quotient_ring
Type of commutative ring in mathematics
In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality
Cohen–Macaulay_ring
Most general completion of a commutative square given two morphisms with same codomain
the category of commutative rings (with identity), the pullback is called the fibered product. Let A, B, and C be commutative rings (with identity) and
Pullback_(category_theory)
Subring consisting of the elements x
the center of a ring R is the subring consisting of the elements x such that xy = yx for all elements y in R. It is a commutative ring and is denoted as
Center_(ring_theory)
Smallest positive number divisible by two integers
multiple can be defined generally over commutative rings as follows: Let a and b be elements of a commutative ring R. A common multiple of a and b is an
Least_common_multiple
Element in a ring whose some power is 0
{\displaystyle R} is called a reduced ring. Every nilpotent element x {\displaystyle x} in a commutative ring is contained in every prime ideal p {\displaystyle
Nilpotent
Square matrices satisfy their characteristic equation
and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies its
Cayley–Hamilton_theorem
Type of integral domain
arithmetic holds. Specifically, a UFD is an integral domain (a nontrivial commutative ring in which the product of any two non-zero elements is non-zero) in which
Unique_factorization_domain
Commutative ring with a well behaved theory of prime factorization
In commutative algebra, a Krull ring, or Krull domain, is a commutative ring with a well behaved theory of prime factorization. They were introduced by
Krull_ring
Ring without non-zero nilpotent elements
A commutative algebra over a commutative ring is called a reduced algebra if its underlying ring is reduced. The nilpotent elements of a commutative ring
Reduced_ring
Construction in homological algebra
variable (from R {\displaystyle R} -modules to abelian groups). For a commutative ring R {\displaystyle R} and R {\displaystyle R} -modules A {\displaystyle
Tor_functor
Ring in abstract algebra
or two-sided Artinian if it is both left and right Artinian. For commutative rings the left and right definitions coincide, but in general they are distinct
Artinian_ring
Construction within abstract algebra
quotient ring or total ring of fractions is a construction that generalizes the notion of the field of fractions of an integral domain to commutative rings R
Total_ring_of_fractions
Overview of and topical guide to algebraic structures
nontrivial commutative ring in which the product of any two nonzero elements is nonzero. Field: a commutative division ring (i.e. a commutative ring which
Outline of algebraic structures
Outline_of_algebraic_structures
Mathematical element
In commutative algebra, an element b of a commutative ring B is said to be integral over a subring A of B if b is a root of some monic polynomial over
Integral_element
Algebraic structure with an associative operation and an identity element
commutative is called a commutative monoid (or, less commonly, an abelian monoid). Commutative monoids are often written additively. Any commutative monoid
Monoid
Analogue of a prime number in a commutative ring
mathematics, specifically in abstract algebra, a prime element of a commutative ring is an object satisfying certain properties similar to the prime numbers
Prime_element
Product of a number by itself
elements. A commutative ring such that the square of a non zero element is never zero is called a reduced ring. More generally, in a commutative ring, a radical
Square_(algebra)
Algebra where division is always defined
meaningful. The real numbers can be extended to a wheel, as can any commutative ring. The term wheel is inspired by the topological picture ⊙ {\displaystyle
Wheel_theory
algebraic geometry, glossary of ring theory and glossary of module theory. In this article, all rings are assumed to be commutative with identity 1. Contents:
Glossary of commutative algebra
Glossary_of_commutative_algebra
Construction in homological algebra
Moreover, for a fixed ring R, Ext is a functor in each variable (contravariant in A, covariant in B). For a commutative ring R and R-modules A and B
Ext_functor
Algebraic structure used in theoretical physics
\mathbb {Z} _{2}} -graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication
Superalgebra
Theorem in algebra mathematics
and commutative algebra, Nakayama's lemma — also known as the Krull–Azumaya theorem — governs the interaction between the Jacobson radical of a ring (typically
Nakayama's_lemma
Mathematical ring whose elements are matrices
matrix ring is again a matrix ring. Over a rng, one can form matrix rngs. When R is a commutative ring, the matrix ring Mn(R) is an associative algebra
Matrix_ring
Abstract algebra concept
to be confused with the quotient of a ring by an ideal, which is a quite different concept. For a commutative ring that is not an integral domain, the analogous
Field_of_fractions
Concept in algebra
In ring theory, a branch of mathematics, the radical of an ideal I {\displaystyle I} of a commutative ring is another ideal defined by the property that
Radical_of_an_ideal
Mathematical concept in polynomial theory
The resultant of two univariate polynomials over a field or over a commutative ring is commonly defined as the determinant of their Sylvester matrix. More
Resultant
Ideal that maps to zero a subset of a module
{\displaystyle R} is a commutative ring and I {\displaystyle I} is an ideal of R {\displaystyle R} , we can consider the quotient ring R / I {\displaystyle
Annihilator_(ring_theory)
In ring theory, a branch of mathematics, the conductor is a measurement of how far apart a commutative ring and an extension ring are. Most often, the
Conductor_(ring_theory)
In algebra, completion w.r.t. powers of an ideal
together they are among the most basic tools in analysing commutative rings. Complete commutative rings have a simpler structure than general ones, and Hensel's
Completion_of_a_ring
Algebraic structure
principal ideal domain, or PID, is an integral domain (that is, a non-zero commutative ring without nonzero zero divisors) in which every ideal is principal (that
Principal_ideal_domain
Number in {..., –2, –1, 0, 1, 2, ...}
{\displaystyle \mathbb {Z} } together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of such algebraic structure
Integer
Generalization of additive and multiplicative inverses
non-unit, the ring is a field if the multiplication is commutative, or a division ring otherwise. In a noncommutative ring (that is, a ring whose multiplication
Inverse_element
Mathematical concept
R^{\text{op}}} is essentially the same as R {\displaystyle R} . All commutative rings are self-opposite. Let us define the antiisomorphism ι : ( R , ⋄
Opposite_ring
Method for specifying point positions
be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated
Coordinate_system
Mathematical concept named for Ernst Witt
elements of a commutative ring. Ernst Witt showed how to put a ring structure on the set of Witt vectors, in such a way that the ring of Witt vectors
Witt_vector
Mathematical group that can be generated as the set of powers of a single element
{\displaystyle \mathbb {Z} } n or Zn, not to be confused with the commutative ring of p-adic numbers), that is generated by a single element. That is
Cyclic_group
Particular kind of algebraic structure
A} be a unital commutative Banach algebra over C . {\displaystyle \mathbb {C} .} Since A {\displaystyle A} is then a commutative ring with unit, every
Banach_algebra
Algebraic structure
as shown by the following chain of class inclusions: rngs ⊃ rings ⊃ commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃
Integrally_closed_domain
In mathematics, a module that has a basis
the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. Given any set S and ring R
Free_module
In algebra, a filtered ring A is said to be almost commutative if the associated graded ring gr A = ⊕ A i / A i − 1 {\displaystyle \operatorname {gr}
Almost_commutative_ring
Mathematics independent of applications
here could be drawn from ring theory. In that subject, one has the subareas of commutative ring theory and non-commutative ring theory. An uninformed observer
Pure_mathematics
Algebraic structure used in analysis
Lie algebra over a field extends to define a Lie algebra over any commutative ring R. Namely, a Lie algebra g {\displaystyle {\mathfrak {g}}} over R is
Lie_algebra
Algebraic structure used in topology
fixed here.) Note that yx = −xy = −[Q], by graded-commutativity. More generally, let R be a commutative ring, and let X and Y be any topological spaces such
Cohomology
Algebraic ring classification
literature refers to a commutative semi-local ring in general as a quasi-semi-local ring, using semi-local ring to refer to a Noetherian ring with finitely many
Semi-local_ring
COMMUTATIVE RING
COMMUTATIVE RING
Girl/Female
Tamil
Anumika | அநà¯à®‚மிகாÂ
Ring finger
Anumika | அநà¯à®‚மிகாÂ
Girl/Female
British, English
Commutative Form of Louise; Renowned in Battle
Surname or Lastname
English
English : from the Old English personal name Hringwulf.German : from a short form of a Germanic personal name based on hring ‘ring’.German : metonymic occupational name for a ring maker (see Ringler).German : altered spelling of Ringel, an Old Prussian personal name.
Surname or Lastname
English
English : from Old Norse drengr ‘young man’, but with more than one possible interpretation. It may reflect the personal name (originally a byname) of this form, which had some currency in the most Scandinavian-influenced areas of medieval England. Alternatively it may reflect the Middle English borrowing of the vocabulary word in the sense ‘servant’, later a technical term of the feudal system of Northumbria for a free tenant who held land by military and agricultural service, sometimes paying rent as well or in commutation.
Surname or Lastname
English
English : variant of Hurst.Jewish (Ashkenazic) : ornamental name or nickname from Polish herszt ‘ringleader’, ‘chieftain’.
Surname or Lastname
English and German
English and German : variant of Ring 1.Perhaps a Rhenish short form of the Latin personal name Quirinus.
Surname or Lastname
English, German, and Jewish (Ashkenazic)
English, German, and Jewish (Ashkenazic) : from the Middle English, German, or Yiddish elements gold + ring. As an English or German surname it is most probably a nickname for someone who wore a gold ring. As a Jewish surname it is generally an ornamental name.Scottish : habitational name from Goldring in the bailiary of Kylestewart.The name is found in England as early as 1230, when Thomas Goldring is recorded as holding property in Essex and Hertfordshire. The name was quite common in London, Sussex, and Hampshire from early times, and descendants of these bearers are now also well established in Canada. The first known bearer in Scotland is Thomas of Goldringe, who held land in Prestwick in 1511.
Surname or Lastname
English
English : habitational name from places in Cumbria, Lincolnshire, and Northamptonshire. The first gets its name from Old English HaferingtÅ«n ‘settlement (Old English tÅ«n) associated with someone called Hæfer’, a byname meaning ‘he-goat’. The second probably meant ‘settlement (Old English tÅ«n) of someone called Hæring’. Alternatively, the first element may have been Old English hæring ‘stony place’ or hÄring ‘gray wood’. The last, recorded in Domesday Book as Arintone and in 1184 as Hederingeton, is most probably named with an unattested Old English personal name, Heathuhere.Irish (County Kerry and the West) : adopted as an Anglicized form of Gaelic Ó hArrachtáin ‘descendant of Arrachtán’, a personal name from a diminutive of arrachtach ‘mighty’, ‘powerful’.Irish (County Kerry) : adopted as an Anglicized form of Gaelic Ó hIongardail, later Ó hUrdáil, ‘descendant of Iongardal’.Irish : reduced Anglicized form of Gaelic Ó hOireachtaigh ‘descendant of Oireachtach’, a byname meaning ‘member of the assembly’ or ‘frequenting assemblies’.
Girl/Female
British, English, German
Commutative Form of Louise; Renowned in Battle
Surname or Lastname
English
English : habitational name from places in Oxfordshire and West Sussex named Goring, from Old English GÄringas ‘people of GÄra’, a short form of the various compound names with the first element gÄr ‘spear’.German (Göring) : see Goering.
Boy/Male
Indian, Malayalam
Commutation
Surname or Lastname
English
English : variant of Kestel.German : from Middle High German kezzel ‘kettle’, ‘cauldron’, hence a metonymic occupational name for a maker of copper cooking vessels, or alternatively a topographic and habitational name, from the same word in the sense ‘(ring-shaped) hollow’.Dutch and Belgian : habitational name from any of the places so named in the Belgian provinces of Antwerp and Limburg or the Dutch province of North Brabant.
Boy/Male
Australian, British, English, French, German, Japanese
Ring; Apple; Peace be with You
Surname or Lastname
English
English : of uncertain origin. It is first attested in Norwich in 1259 as Ringerose, and later forms show no significant variantion. Unless it had already been drastically altered by folk etymology at that early date, it is probably from Middle English ring ‘ring’ + rose ‘rose’, but if so the original meaning is far from clear.
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : from the Old French personal name Reinger, Rainger, composed of the Germanic elements ragin ‘advice’, ‘counsel’ + gÄr, gÄ“r ‘spear’, ‘lance’.English : occupational name for a maker of rings (see Ring 1) or for a bell ringer, from Middle English ring(en) ‘to ring’, Old English hringan.German : occupational name for a turner, someone who made objects by rotating them on a lathe or wheel.
Surname or Lastname
English, German, and Dutch
English, German, and Dutch : metonymic occupational name for a maker of rings (from Middle English ring, Middle High German rinc, Middle Dutch ring), either to be worn as jewelry or as component parts of chain-mail, harnesses, and other objects. In part it may also have arisen as a nickname for a wearer of a ring.Scandinavian : from ring ‘ring’, probably an ornamental name but possibly applied in the same sense as 3 or 1.German : topographic name from Middle High German, Middle Low German rink, rinc ‘circle’.Irish (eastern County Cork) : reduced Anglicized form of Gaelic Ó Rinn (see Reen).
Boy/Male
English
Ring.
Girl/Female
Tamil
Anamika | அநாமிகா
Ring finger, Virtuous, Free of the limitations imposed by a name
Anamika | அநாமிகா
Surname or Lastname
English
English : patronymic from Dear 1.German (Döring) : see Doering.
Surname or Lastname
English
English : patronymic from Dear 1.German : probably a variant of Döring (see Doering).
COMMUTATIVE RING
COMMUTATIVE RING
Girl/Female
Indian
Goddess of wealth
Girl/Female
Biblical
Walking, going.
Girl/Female
English
From the Greek barbaros meaning foreign or strange, traveler from a foreign land. In Catholic...
Boy/Male
Australian, British, English, Greek
Royal
Boy/Male
Tamil
Boy/Male
British, Celtic, English, French
Noble Friend
Girl/Female
Indian, Telugu
Rose
Girl/Female
Sikh
Courtesy of God
Girl/Female
Indian, Turkish
Limit; Short Form of Simran
Girl/Female
Assamese, Hindu, Indian, Kannada, Sindhi, Traditional
River
COMMUTATIVE RING
COMMUTATIVE RING
COMMUTATIVE RING
COMMUTATIVE RING
COMMUTATIVE RING
a.
Ring-streaked.
n.
The change of a penalty or punishment by the pardoning power of the State; as, the commutation of a sentence of death to banishment or imprisonment.
n.
Any one of several species of small plovers of the genus Aegialitis, having a ring around the neck. The ring is black in summer, but becomes brown or gray in winter. The semipalmated plover (Ae. semipalmata) and the piping plover (Ae. meloda) are common North American species. Called also ring plover, and ring-necked plover.
n.
The ring-necked duck.
n.
A contagious affection of the skin due to the presence of a vegetable parasite, and forming ring-shaped discolored patches covered with vesicles or powdery scales. It occurs either on the body, the face, or the scalp. Different varieties are distinguished as Tinea circinata, Tinea tonsurans, etc., but all are caused by the same parasite (a species of Trichophyton).
n.
A sum of money paid formerly to the bishop or archdeacon, now to the ecclesiastical commissioners, by an incumbent, as a commutation for entertainment at the time of visitation; -- called also proxy.
v. i.
To obtain or bargain for exemption or substitution; to effect a commutation.
n.
The act of giving one thing for another; barter; exchange.
n.
Shield money; commutation of service for a sum of money. See Escuage.
n.
A light sail set abaft and beyong the leech of a boom-and-gaff sail; -- called also ringsail.
a.
Having a well defined ring of color around the neck.
a.
Having circular streaks or lines on the body; as, ring-streaked goats.
a.
Adapted or designed to confute.
n.
A substitution, as of a less thing for a greater, esp. a substitution of one form of payment for another, or one payment for many, or a specific sum of money for conditional payments or allowances; as, commutation of tithes; commutation of fares; commutation of copyright; commutation of rations.
a.
Relative to exchange; interchangeable; reciprocal.
n.
The ring finger.
n.
A passing from one state to another; change; alteration; mutation.
n.
See Ringtail, 2.
n.
A game in which the object is to toss a ring so that it will catch upon an upright stick.
n.
One in charge of the performances (as of horses) within the ring in a circus.