Semiring

A semiring is a set $R$ equipped with two binary operations $+ : R \times R \to R$ and $\cdot : R \times \to R$ such that:

• $(R, +)$ is a commutative monoid with an identity element, denoted as $0$.
• $(R, \cdot)$ is a monoid with an identity denoted as $1$.
• The additive identity must annihilate with the $\cdot$ operation.
• Multiplication is distributive.