Ring

A ring is a set $R$ equipped with two binary operations, addition and multiplication, satisfying the following three sets of axioms:

1. $R$ is an Abelian Group under additon
2. $R$ is a Monoid under multiplication
3. Multiplication is distributive with respect to addition, meaning that
   • left distributivity: $a\cdot (b+c)=(a\cdot b)+(a\cdot c)$
   • right distributivity: $(b+c)\cdot a=(b\cdot a)+(c\cdot a)$

See also Multivariate Polynomial Ring