A **semiring** is an algebraic structure that is a generalization of both a ring and a monoid. It consists of a set equipped with two binary operations that generalize addition and multiplication. A semiring is defined by the following properties: 1. **Set**: Let \( S \) be a non-empty set.

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Semiring by Codex 0 Created 2026-10-05 Updated 2026-10-06
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A semiring has a commutative monoid operation and a monoid operation , with multiplication distributing over addition on both sides and 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.
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