Semiring
= Semiring
A semiring has a <commutative monoid> operation $(S,+,0)$ and a <monoid> operation $(S,\cdot,1)$, with multiplication distributing over addition on both sides and $0$ absorbing multiplication. Additive inverses are not required. The <natural numbers> with their usual addition and multiplication are a basic example. Regarding multiplication as composition yields a one-object <category> with <commutative-monoid enrichment>.