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Algebraic structure
appears in the theory of one-parameter operator semigroups: see C0-semigroup. The binary operation of a semigroup is most often denoted multiplicatively: x
Semigroup
Action of a semigroup on a set
computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such
Semigroup_action
Families of certain algebraic structures
mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying
Special_classes_of_semigroups
In algebra, a transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under
Transformation_semigroup
In mathematics, a compact semigroup is a semigroup in which the sets of solutions to equations can be described by finite sets of equations. The term "compact"
Compact_semigroup
Structure in group theory (in mathematics)
In group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse
Inverse_semigroup
Clifford semigroup (sometimes also called "inverse Clifford semigroup") is a completely regular inverse semigroup. It is an inverse semigroup with x x
Clifford_semigroup
Special kind of semigroup in mathematics
In mathematics, a numerical semigroup is a special kind of a semigroup. Its underlying set is the set of all nonnegative integers except a finite number
Numerical_semigroup
In mathematics, a catholic semigroup is a semigroup in which no two distinct elements have the same set of inverses. The terminology was introduced by
Catholic_semigroup
Academic journal
research in semigroup theory. Coverage in the journal includes: algebraic semigroups, topological semigroups, partially ordered semigroups, semigroups of measures
Semigroup_Forum
Algebraic structure
mathematics, an ordered semigroup is a semigroup (S,•) together with a partial order ≤ that is compatible with the semigroup operation, meaning that x
Ordered_semigroup
In mathematics, Arf semigroups are certain subsets of the non-negative integers closed under addition, that were studied by Cahit Arf (1948). They appeared
Arf_semigroup
Semigroup in abstract algebra
mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism
Semigroup_with_involution
Generalization of additive and multiplicative inverses
an I-semigroup and a *-semigroup. A class of semigroups important in semigroup theory are completely regular semigroups; these are I-semigroups in which
Inverse_element
Generalization of the exponential function
In mathematical analysis, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function
C0-semigroup
mathematics known as semigroup theory, an E-semigroup is a semigroup in which the idempotents form a subsemigroup. Certain classes of E-semigroups have been studied
E-semigroup
orthodox semigroup is a regular semigroup whose set of idempotents forms a subsemigroup. In more recent terminology, an orthodox semigroup is a regular
Orthodox_semigroup
Algebraic structure with an associative operation and an identity element
with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of
Monoid
Concept in mathematics
and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup). The study of semigroups as images
Free_monoid
completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. The class of completely regular semigroups forms an important
Completely_regular_semigroup
Mathematical structure that describes the dynamics in a Markovian open quantum system
Markov semigroup describes the dynamics in a Markovian open quantum system. The axiomatic definition of the prototype of quantum Markov semigroups was first
Quantum_Markov_semigroup
In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is
Bicyclic_semigroup
In abstract algebra, a semigroup with three elements is an object consisting of three elements and an associative operation defined on them. The basic
Semigroup_with_three_elements
Rees matrix semigroups are a special class of semigroups introduced by David Rees in 1940. They are of fundamental importance in semigroup theory because
Rees_matrix_semigroup
In mathematics, a topological semigroup is a semigroup that is simultaneously a topological space, and whose semigroup operation is continuous. Every topological
Topological_semigroup
mathematics, the Munn semigroup is the inverse semigroup of isomorphisms between principal ideals of a semilattice (a commutative semigroup of idempotents)
Munn_semigroup
In mathematics, Brandt semigroups are completely 0-simple inverse semigroups. In other words, they are semigroups without proper ideals and which are also
Brandt_semigroup
Semigroup with the cancellation property
In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the
Cancellative_semigroup
In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such
Regular_semigroup
Mathematical structure
In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating
Automatic_semigroup
Algebraic structure with a binary operation
the sense used by Hausmann and Ore. Nevertheless, influential books in semigroup theory, including Clifford and Preston (1961) and Howie (1995) use groupoid
Magma_(algebra)
Abstract algebra concept
{\displaystyle S} is a semigroup/monoid generating set of G {\displaystyle G} if G {\displaystyle G} is the smallest semigroup/monoid containing S {\displaystyle
Generating_set_of_a_group
Algebraic structure in mathematics
mathematics, the four-spiral semigroup is a special semigroup generated by four idempotent elements. This special semigroup was first studied by Karl Byleen
Four-spiral_semigroup
In mathematics, a null semigroup (also called a zero semigroup) is a semigroup with an absorbing element, called zero, in which the product of any two
Null_semigroup
Type of strongly continuous semigroup
In mathematics, an analytic semigroup is particular kind of strongly continuous semigroup. Analytic semigroups are used in the solution of partial differential
Analytic_semigroup
inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on a set
Symmetric_inverse_semigroup
linear or non-linear. Closely related to Markov operators is the Markov semigroup. The definition of Markov operators is not entirely consistent in the
Markov_operator
Extension of "invertibility" in abstract algebra
for the right cancellative or two-sided cancellative properties. In a semigroup, a left-invertible element is left-cancellative, and analogously for right
Cancellation_property
Set endowed with a partial binary operation
partial groupoid ( G , ∘ ) {\displaystyle (G,\circ )} is called a partial semigroup if the following associative law holds: For all x , y , z ∈ G {\displaystyle
Partial_groupoid
Type of semigroup
In mathematics, an aperiodic semigroup is a semigroup S such that every element is aperiodic, that is, for each x in S there exists a positive integer
Aperiodic_semigroup
continuous semigroups that gives a necessary and sufficient condition for a linear operator in a Banach space to generate a contraction semigroup. Let A be
Lumer–Phillips_theorem
Representation theory of the symplectic group
representation leads to a semigroup of contraction operators, introduced as the oscillator semigroup by Roger Howe in 1988. The semigroup had previously been
Oscillator_representation
Semigroup in which every element is idempotent
In mathematics, a band (also called idempotent semigroup) is a semigroup in which every element is idempotent (in other words equal to its own square)
Band_(algebra)
semigroup theory, a Rees factor semigroup (also called Rees quotient semigroup or just Rees factor), named after David Rees, is a certain semigroup constructed
Rees_factor_semigroup
Theorem
continuous one-parameter semigroups of linear operators on Banach spaces. It is sometimes stated for the special case of contraction semigroups, with the general
Hille–Yosida_theorem
Special semigroup of positive rational numbers
In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers. The elements of a generating
3x_+_1_semigroup
Natural number
{\displaystyle a^{1}=a} , so that 1 is also the identity for any power semigroup. 1 is its own factorial 1 ! = 1 {\displaystyle 1!=1} . Moreover, the empty
1
Semigroup containing no elements
In mathematics, a semigroup with no elements (the empty semigroup) is a semigroup in which the underlying set is the empty set. Many authors do not admit
Empty_semigroup
alphabet Σ, or as the induced transformation semigroup of Q. In older books like Clifford and Preston (1967) semigroup actions are called "operands". In category
Semiautomaton
Function that applies a set to itself
function of a set into itself (especially in terms like "transformation semigroup" and similar), there exists an alternative form of terminological convention
Transformation_(function)
Markovian quantum master equation for density matrices (mixed states)
for various times are collectively referred to as a quantum dynamical semigroup—a family of quantum dynamical maps ϕ t {\displaystyle \phi _{t}} on the
Lindbladian
Special types of subgroups encountered in group theory
apply to semigroups. In ring theory, the centralizer of a subset of a ring is defined with respect to the multiplication of the ring (a semigroup operation)
Centralizer_and_normalizer
used with several meanings. In the theory of semigroups, a weak inverse of an element x in a semigroup (S, •) is an element y such that y • x • y = y
Weak_inverse
Topics referred to by the same term
mathematics: the differentiability class C0 a C0-semigroup, a strongly continuous one-parameter semigroup c0, the Banach space of real sequences that converge
C0
Semigroup containing exactly one element
In mathematics, a trivial semigroup (a semigroup with one element) is a semigroup for which the cardinality of the underlying set is one. The number of
Trivial_semigroup
Stochastic process
sup norm is a Banach space. A Feller semigroup on C 0 ( X ) {\textstyle C_{0}(X)} is a contraction C0-semigroup of positive operators on C 0 ( X ) {\textstyle
Feller_process
Partial algebra
requirement that there be an identity at each object. Semigroupoids generalise semigroups in the same way that small categories generalise monoids and groupoids
Semigroupoid
Algebraic structure in semigroup theory
mathematics, a nowhere commutative semigroup is a semigroup S such that, for all a and b in S, if ab = ba then a = b. A semigroup S is nowhere commutative if
Nowhere_commutative_semigroup
Russian-American mathematician (1938–2023)
– 4 October 2023) was a Russian-American mathematician, an expert in semigroups, and a Distinguished Professor in the Department of Mathematical Sciences
Boris_M._Schein
Approach to the study of finite semigroups and automata
finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and
Krohn–Rhodes_theory
Example of a Semigroup
a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. There are exactly five nonisomorphic semigroups having
Semigroup_with_two_elements
In mathematics, and more precisely in semigroup theory, a variety of finite semigroups is a class of semigroups satisfying specific algebraic properties
Variety_of_finite_semigroups
Topics referred to by the same term
theory of numerical semigroups, the genus of a numerical semigroup is the cardinality of the set of gaps in the numerical semigroup Genus of a quadratic
Genus_(disambiguation)
Functional equation characterizing associative binary operations
associative in the usual algebraic sense, and therefore underlies the study of semigroups and many kinds of aggregation operators. When additional regularity conditions
Associativity_equation
Generalized function whose value is zero everywhere except at zero
Convolution semigroups in L1 that approximate the delta function are always an approximation to the identity in the above sense, however the semigroup condition
Dirac_delta_function
Algebraic structure
n variables: R[Nn] =: R[X1, ..., Xn]. If G is a semigroup, the same construction yields a semigroup ring R[G]. Free algebra Puiseux series Lang, Serge
Monoid_ring
Function whose actual domain of definition may be smaller than its apparent domain
{\displaystyle X,} forms a regular semigroup called the semigroup of all partial transformations (or the partial transformation semigroup on X {\displaystyle X} )
Partial_function
presentation of a monoid (or a presentation of a semigroup) is a description of a monoid (or a semigroup) in terms of a set Σ of generators and a set of
Presentation_of_a_monoid
Term in mathematics
subgroups. In semigroup theory, a maximal subgroup of a semigroup S is a subgroup (that is, a subsemigroup which forms a group under the semigroup operation)
Maximal_subgroup
Method for solving partial differential equations
linear operator on a Banach space and generates a strongly continuous semigroup ( S ( t ) ) t ≥ 0 {\displaystyle (S(t))_{t\geq 0}} . In that case the
Duhamel's_principle
Mathematical property of algebraic structures
In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some
Archimedean_property
Algorithm for fast exponentiation
positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred
Exponentiation_by_squaring
Mathematical structure with greatest common divisors
GCD-semigroup. A GCD-semigroup is a semigroup with the additional property that for any a {\displaystyle a} and b {\displaystyle b} in the semigroup S {\displaystyle
GCD_domain
Turkish mathematician (1910–1997)
theory) in topology, the Hasse–Arf theorem in ramification theory, Arf semigroups and Arf rings. Cahit Arf was born on 11 October 1910 in Thessaloniki,
Cahit_Arf
Branch of mathematics that studies algebraic structures
lemma Semigroup Subsemigroup Free semigroup Green's relations Inverse semigroup (or inversion semigroup, cf. [1]) Krohn–Rhodes theory Semigroup algebra
List of abstract algebra topics
List_of_abstract_algebra_topics
Operation on mathematical functions
transformation semigroup or symmetric semigroup on X. (One can actually define two semigroups depending how one defines the semigroup operation as the
Function_composition
Structure-preserving map between two algebraic structures of the same type
the second structure. For example: A semigroup homomorphism is a map between semigroups that preserves the semigroup operation. A monoid homomorphism is
Homomorphism
Index of articles associated with the same name
every congruence on a semigroup is associated with an ideal, so a simple semigroup may have nontrivial congruences. A semigroup with no nontrivial congruences
Simple_(abstract_algebra)
Differential operator in mathematics
is a strongly continuous contraction semigroup whose generator is the Laplacian; more generally, the heat semigroup acts contractively on Lp for 1 ≤ p ≤
Laplace_operator
Algebraic structure
bi-commutative, bisymmetric, surcommutative, entropic, etc. Any commutative semigroup is a medial magma, and a medial magma has an identity element if and only
Medial_magma
holomorphic univalent self-mappings of the unit disk, called a Loewner semigroup. This semigroup corresponds to a time dependent holomorphic vector field on the
Loewner_differential_equation
Mathematical conjecture
their conjecture was proven in 2007 by Avraham Trahtman. A transformation semigroup is synchronizing if it contains an element of rank 1, that is, an element
Synchronizing_word
Bounded operators with sub-unit norm
continuous contraction semigroup T(t) (t ≥ 0) on a Hilbert space H. Cooper (1947) had previously proved the result for one-parameter semigroups of isometries.
Contraction_(operator_theory)
Computing problem
[citation needed] When the function of interest in a range query is a semigroup operator, the notion of f − 1 {\displaystyle f^{-1}} is not always defined
Range query (computer science)
Range_query_(computer_science)
Class of algebraic structures
are homomorphisms. The class of all semigroups forms a variety of algebras of signature (2), meaning that a semigroup has a single binary operation. A sufficient
Variety_(universal_algebra)
Theorem in convex and algebraic geometry
(this follows from the fact that the prime spectrum of the semigroup algebra of such a semigroup is, by definition, an affine toric variety). The lemma is
Gordan's_lemma
Compact topological semigroup
mathematics, the Ellis–Numakura lemma states that if S is a non-empty semigroup with a topology such that S is a compact space and the product is semi-continuous
Ellis–Numakura_lemma
Overview of and topical guide to algebraic structures
groupoid: S and a single binary operation over S. Semigroup: an associative magma. Monoid: a semigroup with identity element. Group: a monoid with a unary
Outline of algebraic structures
Outline_of_algebraic_structures
Special type of element of a set
element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because there is
Absorbing_element
precisely in semigroup theory, a nilsemigroup or nilpotent semigroup is a semigroup whose every element is nilpotent. Formally, a semigroup S is a nilsemigroup
Nilsemigroup
commuting graph of a semigroup, or in particular of a group, is an undirected graph in which the vertices are elements of the semigroup and there is an edge
Commuting_graph
American mathematician (1957–2022)
was a U.S. and Russian mathematician working in geometric group theory, semigroup theory and combinatorial algebra. He was a Centennial Professor of Mathematics
Mark_Sapir
Mathematical category formed by reversing morphisms
Given a semigroup (S, ·), one usually defines the opposite semigroup as (S, ·)op = (S, *) where x*y ≔ y·x for all x,y in S. So also for semigroups there
Opposite_category
representation as dilations of a univalent holomorphic mapping, or a semigroup of mappings, of the unit disk in the complex numbers into itself. Let
Koenigs_function
problem is uniformly well posed, then the associated semigroup U ( t ) {\displaystyle U(t)} is a C0-semigroup in X {\displaystyle X} . Conversely, if A {\displaystyle
Abstract differential equation
Abstract_differential_equation
Operation in group theory
at least P.) In a semigroup S, the product of two subsets defines a structure of a semigroup on P(S), the power set of the semigroup S; furthermore P(S)
Product_of_group_subsets
residue fields, is an isomorphism of schemes. A semigroup is said to be seminormal if its semigroup algebra is seminormal. Swan, Richard G. (1980), "On
Seminormal_ring
relations are five equivalence relations that characterise the elements of a semigroup in terms of the principal ideals they generate. The relations are named
Green's_relations
Algebraic element satisfying some of the criteria of an inverse
mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes generalized inverses of a matrix A {\displaystyle
Generalized_inverse
Branch of mathematics
twentieth century. The fundamental notion involved is that of an arithmetic semigroup, which is a commutative monoid G satisfying the following properties:
Abstract analytic number theory
Abstract_analytic_number_theory
SEMIGROUP
SEMIGROUP
SEMIGROUP
SEMIGROUP
Boy/Male
Arabic
Beautiful; Gorgeous
Girl/Female
British, English, French
Court-dweller
Male
Greek
(Ανδώνιος) Greek form of Latin Antonius, possibly ANDONIOS means "invaluable."Â
Male
Spanish
Portuguese and Spanish form of German Raginmund, RAYMUNDO means "wise protector."
Boy/Male
Muslim
Sweet, Cute
Girl/Female
Norse
Freya's necklace.
Girl/Female
American, Australian, Chinese, Christian, French, German, Greek, Latin
Nobility; Similar to Alice; Noble Sort
Boy/Male
Sikh
The God of peace
Girl/Female
Australian, Chinese
Clever
Boy/Male
Indian
Public speaker, Singer
SEMIGROUP
SEMIGROUP
SEMIGROUP
SEMIGROUP
SEMIGROUP