Ring

A ring is a semiring where each element has an additive inverse.

Remarks

A ring is a set $R$ equipped with two binary operations $+$ and $\cdot$ satisfying the following three sets of axioms, called the ring axioms:

• $(R, +)$ is an abelian group under addition.
• $(R, \cdot)$ is a monoid under multiplication.
• $*$ is distributive.