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Search references for SEMIRING. Phrases containing SEMIRING
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Algebraic ring that need not have additive negative elements
semiring called the trivial semiring. This triviality can be characterized via 0 = 1 {\displaystyle 0=1} and so when speaking of nontrivial semirings
Semiring
Semiring with minimum and addition replacing addition and multiplication
In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing
Tropical_semiring
Mathematical ring whose elements are matrices
only a semiring for Mn(R) to be defined. In this case, Mn(R) is a semiring, called the matrix semiring. Similarly, if R is a commutative semiring, then
Matrix_ring
Generalization of vector spaces from fields to rings
modules are still possible. In particular, for any semiring S, the matrices over S form a semiring over which the tuples of elements from S are a module
Module_(mathematics)
Semiring arising in tropical analysis
In mathematics, in the field of tropical analysis, the log-semiring is the semiring structure on the logarithmic scale, obtained by considering the extended
Log_semiring
Truncating subtraction on natural numbers, or a generalization thereof
monoid is a commutative monoid with monus, the semiring is called a semiring with monus, or m-semiring. If M is an ideal in a Boolean algebra, then M
Monus
mathematics, a near-semiring, also called a seminearring, is an algebraic structure more general than a near-ring or a semiring. Near-semirings arise naturally
Near-semiring
Semiring defined over probabilities
The Viterbi semiring is a commutative semiring defined over the set of probabilities (typically the interval [ 0 , 1 ] {\displaystyle [0,1]} ) with addition
Viterbi_semiring
Algebraic structure with addition and multiplication
The natural numbers (including 0) form an algebraic structure known as a semiring (which has all of the axioms of a ring excluding that of an additive inverse)
Ring_(mathematics)
generally, all complete semirings are quasiregular. The term closed semiring is actually used by some authors to mean complete semiring rather than just quasiregular
Quasiregular_element
Skeletonized version of algebraic geometry
semiring. This is defined in two ways, depending on max or min convention. The min tropical semiring T {\displaystyle \mathbb {T} } is the semiring T
Tropical_geometry
Idempotent semiring endowed with a closure operator
Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is a semiring that generalizes the theory of regular expressions: it consists of a set
Kleene_algebra
Family closed under unions and relative complements
to the modern theory of probability and the definition of measures. A semiring (of sets) is a family of sets S {\displaystyle {\mathcal {S}}} with the
Ring_of_sets
Area of math
analysis is the study of idempotent semirings, such as the tropical semiring. The lack of an additive inverse in the semiring is compensated somewhat by the
Idempotent_analysis
Array of numbers
applies to matrices with entries in a semiring without modification. Matrices of fixed size with entries in a semiring form a commutative monoid Mat ( m
Matrix_(mathematics)
Study of the tropical semiring
analysis, tropical analysis is the study of the tropical semiring. The max tropical semiring can be used appropriately to determine marking times within
Tropical_analysis
Subset of real numbers that are greater than zero
{\displaystyle \mathbb {R} _{\geq 0}} has a semiring structure (0 being the additive identity), known as the probability semiring; taking logarithms (with a choice
Positive_real_numbers
Set with operations obeying given axioms
multiplication, with multiplication distributing over addition. Ring: a semiring whose additive monoid is an abelian group. Division ring: a nontrivial
Algebraic_structure
Database theory algorithm
Boolean semiring (the elimination of a tuple corresponds to a False value in the semiring), but its correctness is maintained if we use any other semiring. For
Yannakakis_algorithm
Algebra where division is always defined
A wheel can be regarded as the equivalent of a commutative ring (and semiring) where addition and multiplication are not a group but respectively a commutative
Wheel_theory
Abstract algebra concept
\mathbb {T} } denote the tropical semiring and let R = T [ X ] {\displaystyle R=\mathbb {T} [X]} be the polynomial semiring over T {\displaystyle \mathbb
Field_of_fractions
Smooth approximation of one-hot arg max
arg min, corresponding to using the log semiring instead of the max-plus semiring (respectively min-plus semiring), and recovering the arg max or arg min
Softmax_function
Computational problem of graph theory
approach to these is to consider the two operations to be those of a semiring. Semiring multiplication is done along the path, and the addition is between
Shortest_path_problem
Cryptography using tropical algebra
mathematical object at the heart of tropical cryptography is the tropical semiring ( R ∪ { ∞ } , ⊕ , ⊗ ) {\displaystyle (\mathbb {R} \cup \{\infty \},\oplus
Tropical_cryptography
Algebraic structure
In mathematics, a semimodule over a semiring R is an algebraic structure analogous to a module over a ring, with the exception that it forms only a commutative
Semimodule
Property involving two mathematical operations
Distributivity is most commonly found in semirings, notably the particular cases of rings and distributive lattices. A semiring has two binary operations, commonly
Distributive_property
Algebraic structure
extended by an absorbing 0, forming the probability semiring, which is isomorphic to the log semiring. Rational functions of the form f /g, where f and
Semifield
Algebraic structure with an associative operation and an identity element
monoid. Cartesian monoid Green's relations Monad (functional programming) Semiring and Kleene algebra Star height problem Vedic square Frobenioid If both
Monoid
Algebraic structure of set algebra
{F}}} ∅ ∈ F {\displaystyle \varnothing \in {\mathcal {F}}} F.I.P. π-system Semiring Never Semialgebra (semifield) Never Monotone class only if A i ↘ {\displaystyle
Σ-algebra
Mathematical function, inverse of an exponential function
addition (LogSumExp), giving an isomorphism of semirings between the probability semiring and the log semiring. Logarithmic one-forms df/f appear in complex
Logarithm
Mathematical operation in linear algebra
requires that the entries belong to a semiring, and does not require multiplication of elements of the semiring to be commutative. In many applications
Matrix_multiplication
Infinite sum that is considered independently from any notion of convergence
Magnus ring over R. Given an alphabet Σ {\displaystyle \Sigma } and a semiring S {\displaystyle S} . The formal power series over S {\displaystyle S}
Formal_power_series
Smooth approximation to the maximum function
family. In tropical analysis, this is the sum in the log semiring. Logarithmic mean Log semiring Smooth maximum Softmax function Zhang, Aston; Lipton, Zack;
LogSumExp
Type of algebraic structure
K , + K , × K ) {\displaystyle (K,+_{K},\times _{K})} be an arbitrary semiring and ( R , ⋅ , ϕ ) {\displaystyle (R,\cdot ,\phi )} a graded monoid. Then
Graded_ring
Family closed under complements and countable disjoint unions
{F}}} ∅ ∈ F {\displaystyle \varnothing \in {\mathcal {F}}} F.I.P. π-system Semiring Never Semialgebra (semifield) Never Monotone class only if A i ↘ {\displaystyle
Dynkin_system
Overview of and topical guide to algebraic structures
0 x = 0 for all x. Near-ring: a semiring whose additive monoid is a (not necessarily abelian) group. Ring: a semiring whose additive monoid is an abelian
Outline of algebraic structures
Outline_of_algebraic_structures
Unary operation on string sets
union) in the algebraic structure itself by the notion of complete star semiring. Wildcard character Glob (programming) It is called "strings" for historical
Kleene_star
and state machines by mapping the edges of a directed graph to a ring or semiring. A single edge weight might represent an array of impulse responses of
Noncommutative signal-flow graph
Noncommutative_signal-flow_graph
Finite state machine with two tapes (input, output)
the set of weights to form a semiring. Two typical semirings used in practice are the log semiring and tropical semiring: nondeterministic automata may
Finite-state_transducer
Function in algebra
addition form a semiring, called the min tropical semiring, and a valuation v is almost a semiring homomorphism from K to the tropical semiring, except that
Valuation_(algebra)
Algebraic structure in linear algebra
and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie
Vector_space
Mathematical problem
semiring, except there are no axioms about additive identities in Tarski's axioms either. However, some authors use the term rig to mean a semiring with
Tarski's high school algebra problem
Tarski's_high_school_algebra_problem
Number used for counting
{\displaystyle \mathbb {N} } is not a ring; instead it is a semiring (also known as a rig). Semirings are an algebraic generalization of rings where multiplication
Natural_number
Family of sets closed under intersection
{F}}} ∅ ∈ F {\displaystyle \varnothing \in {\mathcal {F}}} F.I.P. π-system Semiring Never Semialgebra (semifield) Never Monotone class only if A i ↘ {\displaystyle
Pi-system
Species of butterfly
Pseudacraea semire, the green false acraea, is a butterfly in the family Nymphalidae. It is found in Guinea, Sierra Leone, Liberia, Ivory Coast, Ghana
Pseudacraea_semire
Finite-state machine where edges carry weights
definition of a weighted automaton is generally given over an arbitrary semiring R {\displaystyle R} , an abstract set with an addition operation ⊕ {\displaystyle
Weighted_automaton
Axioms for the natural numbers
·, 1, 0, ≤) is an ordered semiring; because there is no natural number between 0 and 1, it is a discrete ordered semiring. The axiom of induction is
Peano_axioms
Let R be a semiring and A a finite alphabet. A non-commutative polynomial over A is a finite formal sum of words over A. They form a semiring R ⟨ A ⟩ {\displaystyle
Rational_series
Property of operations
idempotent. In a Boolean ring, multiplication is idempotent. In a tropical semiring, addition is idempotent. In a ring of quadratic matrices, the determinant
Idempotence
Algebraic structure in mathematics
disjunction or symmetric difference (not disjunction ∨, which would constitute a semiring). Conversely, every Boolean algebra gives rise to a Boolean ring. Boolean
Boolean_ring
Tensor product of algebras over a field; itself another algebra
Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield Commutative algebra Commutative rings • Integral domain • Integrally
Tensor_product_of_algebras
Measurement scale based on orders of magnitude
Level (logarithmic quantity) Log–log plot Logarithm Logarithmic mean Log semiring Preferred number Semi-log plot Order of magnitude Entropy Entropy (information
Logarithmic_scale
Algebraic structure in mathematics
more general geometrical constructions. Near-field (mathematics) Semiring Near-semiring G. Pilz, (1982), "Near-Rings: What They Are and What They Are Good
Near-ring
Algebraic structure
Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield Commutative algebra Commutative rings • Integral domain • Integrally
Composition_ring
Mathematical structure with greatest common divisors
and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie
GCD_domain
Property in general topology
{F}}} ∅ ∈ F {\displaystyle \varnothing \in {\mathcal {F}}} F.I.P. π-system Semiring Never Semialgebra (semifield) Never Monotone class only if A i ↘ {\displaystyle
Finite_intersection_property
75 Park Seo-yun South Korea 77 Elín Elmarsdóttir Van Pelt Iceland 78 Semire Dauti Albania 82 Sonja Li Kristinsdóttir Iceland 85 Kiana Kryeziu Kosovo
Alpine skiing at the 2026 Winter Olympics – Women's slalom
Alpine_skiing_at_the_2026_Winter_Olympics_–_Women's_slalom
Joining of strings in a programming language
null string. Sets of strings with concatenation and alternation form a semiring, with concatenation distributing over alternation. The identity for alternation
Concatenation
Concept in mathematics
and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie
Map_of_lattices
Theoretical framework for analysing performance guarantees in computer networks
min-plus algebra. Network calculus makes an intensive use on the min-plus semiring (sometimes called min-plus algebra). In filter theory and linear systems
Network_calculus
Function from sets to numbers
{F}}} ∅ ∈ F {\displaystyle \varnothing \in {\mathcal {F}}} F.I.P. π-system Semiring Never Semialgebra (semifield) Never Monotone class only if A i ↘ {\displaystyle
Set_function
isomorphic to an ordered semiring. However, an ordered semiring deduced from a Peano structure may be isomorphic to another ordered semiring. Such relation between
Equivalent definitions of mathematical structures
Equivalent_definitions_of_mathematical_structures
Set without nontrivial polynomial equalities
Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield Commutative algebra Commutative rings • Integral domain • Integrally
Algebraic_independence
Sum of an (infinite) geometric progression
geometric series of elements of abstract algebraic fields, rings, and semirings. A geometric series is a series derived from a special type of sequence
Geometric_series
Branch of mathematics
A + A = A. Tropical analysis – analysis of the idempotent semiring called the tropical semiring (or max-plus algebra/min-plus algebra). Constructive analysis
Mathematical_analysis
Algebraic concept in measure theory, also referred to as an algebra of sets
{F}}} ∅ ∈ F {\displaystyle \varnothing \in {\mathcal {F}}} F.I.P. π-system Semiring Never Semialgebra (semifield) Never Monotone class only if A i ↘ {\displaystyle
Field_of_sets
Family of sets closed under countable unions
{F}}} ∅ ∈ F {\displaystyle \varnothing \in {\mathcal {F}}} F.I.P. π-system Semiring Never Semialgebra (semifield) Never Monotone class only if A i ↘ {\displaystyle
Sigma-ring
Vector space equipped with a bilinear product
and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie
Algebra_over_a_field
Special type of element of a set
semigroups, especially the multiplicative semigroup of a semiring. In the case of a semiring with 0 {\displaystyle 0} , the definition of an absorbing
Absorbing_element
API for graph data and graph operations
domain of double-precision floating point numbers with GrB_Semiring_new(&min_plus_semiring, GrB_MIN_FP64, GrB_PLUS_FP64). While the GraphBLAS specification
GraphBLAS
Kind of finite-state machine
automata from rational patterns, functions and relations expressed in semiring algebraic terms. The example below shows a binary rational function equivalent
Event-driven finite-state machine
Event-driven_finite-state_machine
1747 novella by Voltaire
protagonist, a Babylonian philosopher. Sémire – Zadig's original love interest. Orcan – Zadig's rival for Sémire and nephew of a certain Minister of State
Zadig
Type of algebras, possibly non associative
and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie
Composition_algebra
Algebraic structure
references in Udo Hebisch and Hanns Joachim Weinert, Semirings and Semifields, in particular, Section 10, Semirings with infinite sums, in M. Hazewinkel, Handbook
Semigroup
Number in {..., –2, –1, 0, 1, 2, ...}
Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield Commutative algebra Commutative rings • Integral domain • Integrally
Integer
Proof assistant
example, the "ring" tactic decides the theory of equality modulo ring or semiring axioms via associative-commutative rewriting. For example, the following
Rocq
Any collection of sets, or subsets of a set
{F}}} ∅ ∈ F {\displaystyle \varnothing \in {\mathcal {F}}} F.I.P. π-system Semiring Never Semialgebra (semifield) Never Monotone class only if A i ↘ {\displaystyle
Family_of_sets
German mathematician and educator
[Additive, commutative, and idempotent semirings with the factor condition], concerned the theory of semirings and was supervised by Hanns J. Weinert
Dörte_Haftendorn
Algebraic structure with a binary operation
and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie
Magma_(algebra)
Mathematical term in group theory
Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield Commutative algebra Commutative rings • Integral domain • Integrally
Prüfer_group
Theoretical object in mathematics
tropical geometry, via the fact that semirings (in particular, tropical semirings) arise as quotients of some monoid semiring N[A] of finite formal sums of elements
Field_with_one_element
Algebraic ring without a multiplicative identity
unital algebra containing A, in the sense of universal constructions. Semiring Jacobson (1989), pp. 155–156 Noether (1921), p. 30, §1.2 Dorroh (1932)
Rng_(algebra)
Algebraic structure
and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie
Finite_field
multiplication, N ∪ { ∞ } {\displaystyle \mathbb {N} \cup \{\infty \}} is a semiring but not a ring, as ∞ {\displaystyle \infty } lacks an additive inverse
Extended_natural_numbers
Branch of mathematics
Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield Commutative algebra Commutative rings • Integral domain • Integrally
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Generalization of a measure
{\displaystyle {\mathcal {A}}} is chosen to be a ring of sets or to be at least a semiring of sets in which case some additional properties can be deduced which are
Content_(measure_theory)
Algebraic structure
Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield Commutative algebra Commutative rings • Integral domain • Integrally
Polynomial_ring
Mathematical model of computation
problem to graphs with edges weighted by the elements of an (arbitrary) semiring.[jargon] An example of an accepting state appears in Fig. 5: a deterministic
Finite-state_machine
quasi-Frobenius rings and local rings are usually not semiprimitive. semiring A semiring : An algebraic structure satisfying the same properties as a ring
Glossary_of_ring_theory
Subset of a ring that forms a ring itself
Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield Commutative algebra Commutative rings • Integral domain • Integrally
Subring
Flat horse race in France
Mednaya Violette 2004 Stella Blue Mirabilis Arabian Spell 2003 Dalna Malaica La Ina 2002 White Rose The Wise Lady Semire 2001 Contemporary Glia Urgele
Prix_Miesque
"A Brief History of Algebra with a Focus on the Distributive Law and Semiring Theory". arXiv:1807.11704 [math.HO]. Victor J. Katz, Bill Barton (October
History_of_algebra
Branch of mathematics that studies algebraic structures
ring Algebra over a field Non-associative algebra Relatives to rings: Semiring, Nearring, Rig (algebra) Subring, Subalgebra Center (algebra) Ring ideal
List of abstract algebra topics
List_of_abstract_algebra_topics
Relationship between elements of two sets
X = Y {\displaystyle X=Y} ) form a matrix semiring (indeed, a matrix semialgebra over the Boolean semiring) where the identity matrix corresponds to the
Binary_relation
Concept in mathematics regarding sets operating on groups
and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie
Group_with_operators
Set function that is a precursor to a measure
{F}}} ∅ ∈ F {\displaystyle \varnothing \in {\mathcal {F}}} F.I.P. π-system Semiring Never Semialgebra (semifield) Never Monotone class only if A i ↘ {\displaystyle
Pre-measure
Mathematical structure in abstract algebra
*-invariant: x ∈ I ⇒ x* ∈ I and so on. *-rings are unrelated to star semirings in the theory of computation. A *-algebra A is a *-ring, with involution
*-algebra
Design pattern in functional programming to build generic types
near-semiring, and some additive monads do qualify as such. However, not all additive monads meet the distributive laws of even a near-semiring. In Haskell
Monad (functional programming)
Monad_(functional_programming)
Submodule of a mathematical ring
Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield Commutative algebra Commutative rings • Integral domain • Integrally
Ideal_(ring_theory)
Algebra describing information processing
Constraints form an information algebra (Jaffar & Maher 1994). Semiring valued algebras: C-Semirings induce information algebras (Bistarelli, Montanari &
Information_algebra
SEMIRING
SEMIRING
SEMIRING
SEMIRING
Girl/Female
Tamil
Dharavira | தராவீரா
Boy/Male
African, Indian
Child
Girl/Female
Hindu
Hobby, Luster, Beauty
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Poet
Girl/Female
Scottish
From the French 'bon' meaning good. In Scottish usage 'bonnie' means pretty or charming.
Girl/Female
Hebrew
God's favor.
Boy/Male
Tamil
Tune, New rule
Male
Norwegian
Danish and Norwegian form of Old Norse Þorsteinn, THORSTEIN means "Thor's stone."
Boy/Male
Tamil
Acaryasuta | அகாரà¯à®¯à®¸à¯à®¤à®¾Â
Son of the teacher, Another name of asvatthaman
Male
Scottish
 Pet form of Scottish Raibeart, RAB means "bright fame." Compare with another form of Rab.
SEMIRING
SEMIRING
SEMIRING
SEMIRING
SEMIRING
a.
Having the intrinsic muscles of the larynx attached to the middle of the semirings.
n.
One of the incomplete rings of the upper part of the bronchial tubes of most birds. The semerings form an essential part of the syrinx, or musical organ, of singing birds.