Commutative unital ring

Definition
A commutative unital ring is a set $$R$$ endowed with two binary operations $$+$$ and $$*$$, and constants $$0$$ and $$1$$ such that:


 * $$R$$ is an Abelian group under $$+$$, with identity element $$0$$
 * $$R$$ is an Abelian monoid under $$*$$, with identity element $$1$$
 * Left and right distributivity laws hold:

$$a * (b + c) = (a * b) + (a * c)$$

and:

$$(a + b) * c = (a * c) + (b * c)$$