Editing Semiring (section)

{{About|algebraic structures||Ring of sets#semiring}}
{{Short description|Algebraic ring that need not have additive negative elements}}
{{Ring theory sidebar}}
In [[abstract algebra]], a '''semiring''' is an [[algebraic structure]]. Semirings are a generalization of [[Ring (algebra)|rings]], dropping the requirement that each element must have an [[additive inverse]]. At the same time, semirings are a generalization of [[Lattice (order)#Bounded lattice|bounded]] [[distributive lattice]]s.

The smallest semiring that is not a ring is the [[two-element Boolean algebra]], for instance with [[logical disjunction]] <math>\lor</math> as addition. A motivating example that is neither a ring nor a lattice is the set of [[natural number]]s <math>\N</math> (including zero) under ordinary addition and multiplication. Semirings are abundant because a suitable multiplication operation arises as the [[function composition]] of [[endomorphism]]s over any [[commutative monoid]].

{{Algebraic structures |Ring}}