About: Semiring

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In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. The term rig is also used occasionally—this originated as a joke, suggesting that rigs are rings without negative elements, similar to using rng to mean a ring without a multiplicative identity. Tropical semirings are an active area of research, linking algebraic varieties with piecewise linear structures.

Attributes	Values
rdf:type	Thing building
rdfs:label	Semiring (en)
rdfs:comment	In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. The term rig is also used occasionally—this originated as a joke, suggesting that rigs are rings without negative elements, similar to using rng to mean a ring without a multiplicative identity. Tropical semirings are an active area of research, linking algebraic varieties with piecewise linear structures. (en)
rdfs:seeAlso	Ring of sets
sameAs	Semiring Semiring
dbp:wikiPageUsesTemplate	dbt:Algebraic_structures dbt:Anchor dbt:Annotated_link dbt:Authority_control dbt:Citation dbt:Citation_needed dbt:Cite_book dbt:Cite_journal dbt:Doi dbt:Efn dbt:Em dbt:Noteslist dbt:Reflist dbt:Ring_theory_sidebar dbt:See_also dbt:Sfn dbt:Short_description dbt:Sup dbt:Visible_anchor dbt:Isbn dbt:Unordered_list dbt:Zwj dbt:MathSciNet dbt:Durrett_Probability_Theory_and_Examples_5th_Edition
Subject	Algebraic structures Ring theory
gold:hypernym	Structure
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Semiring?oldid=1072826094&ns=0
Wikipage page ID	371468 (xsd:integer)
page length (characters) of wiki page	33283 (xsd:nonNegativeInteger)
Wikipage revision ID	1072826094 (xsd:integer)
has abstract	In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. The term rig is also used occasionally—this originated as a joke, suggesting that rigs are rings without negative elements, similar to using rng to mean a ring without a multiplicative identity. Tropical semirings are an active area of research, linking algebraic varieties with piecewise linear structures. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Semiring
is Wikipage redirect of	Probability semiring Boolean semiring Semi-ring of sets Starsemiring Dioid Commutative semiring Complete semiring Complete star semiring Continuous semiring Conway semiring Idempotent semiring Hemiring Star semiring Iteration semiring Semi-ring Semi ring Semialgebra Semirings C-semiring Pre-semiring Rig (algebra) Rig (mathematics) Idempotent semi-ring Constraint-based semiring
is Link from a Wikipage to another Wikipage of	Formal power series Green's relations Log semiring Logarithm Logical matrix Non-standard model of arithmetic Noncommutative signal-flow graph Nonstandard analysis 0.999... Absorbing element Algebraic structure Binary relation Binomial theorem Boolean ring Boolean semiring Monoid Monus Carathéodory's extension theorem Free object Generalized distributive law Glossary of areas of mathematics Glossary of ring theory Difference bound matrix Dioid Distributive property Combinatorial class Commutative semiring Complete semiring Complete star semiring Concatenation Content (measure theory) Continuous semiring Conway semiring Dörte Haftendorn Cubic function Finite-state machine

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