Semiring

A semiring is an algebraic structure (S, +, ·) with two binary operations: addition (+) forming a commutative monoid with identity 0, and multiplication (·) forming a monoid with identity 1 (possibly the same as 0 only in the trivial case), where multiplication distributes over addition from both sides and 0 annihilates S under multiplication. Additive inverses need not exist.