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Semiring

In abstract algebra, a semiring is an algebraic structure. Semirings are a generalization of rings, dropping the requirement that each element must have an additive inverse. At the same time, semirings are a generalization of bounded distributive lattices.

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Overview

Terminology

Definition

Construction of new semirings

Properties

Star semirings

Examples

Applications

Generalizations

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Semiring

Nodes169
Edges168
Triples82
Avg. degree1.99
Density0.011834
Components1

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Semiring

Top relations

related to Examples · 18
Semiring → Also, Any, Boolean, By, For, In, It, Likewise, Neither, New, Now, One, Similarly, The, The Viterbi, These, They, This
is a · 10
Semiring → algebraic structure, Conway semiring satisfying the Conway group axioms, empty set, idempotent semiring and with addition defined over arbitrary sets.An additively idempotent semiring with idempotent multiplication, semiring for which the additive monoid is a complete monoid, semiring isomorphic to a sub-semiring of a Boolean algebra.The commutative semiring formed by the two-element Boolean algebra and defined by 1, semiring with an additional unary operator, set R, star semiring satisfying the sum-star and product-star equations, sub-semiring and being commutative is equivalent to being its own center.The commutative semiring of natural numbers is the initial object among its kind
related to Terminology · 8
Semiring → Akin, Baccelli, It, Kuntzmann, Some, The, These, This
has application · 7
Semiring → Markov, Similarly, The, The Floyd, These, Viterbi, Warshall
related to Properties · 7
Semiring → Also, Considering, Further, In, Reflexivity, Some, The
related to Rings · 6
Semiring → Any, As, Here, Note, The, This
related to Star semirings · 6
Semiring → Kleene, Several, The, The Boolean, They, This
related to Construction of new semirings · 5
Semiring → As, Now, Taking, The, This
related to Generalizations · 5
Semiring → Hessenberg, However, Just, Such, Yet
related to Commutative semirings · 3
Semiring → It, Its, The

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Important terminology

displaystyle addition multiplication set mathbb commutative also semirings ring order given zero monoid defined leq idempotent one elements cdot form

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Semiringis aalgebraic structure0.90text
Semiringis aset R0.90text
Semiringis asub-semiring and being commutative is equivalent to being its own center.The commutative semiring of natural numbers is the initial object among its kind0.90text
Semiringis aidempotent semiring and with addition defined over arbitrary sets.An additively idempotent semiring with idempotent multiplication0.90text
Semiringis asemiring for which the additive monoid is a complete monoid0.90text
Semiringis asemiring with an additional unary operator0.90text
Semiringis astar semiring satisfying the sum-star and product-star equations0.90text
Semiringis aConway semiring satisfying the Conway group axioms0.90text
Semiringis asemiring isomorphic to a sub-semiring of a Boolean algebra.The commutative semiring formed by the two-element Boolean algebra and defined by 10.90text
Semiringis aempty set0.90text
commutativity simplify the axioms.Given a strict total orderinstance ofAdditional properties0.80text
Semiringhas applicationThe0.60section

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