Ring is an algebraic structure defined as 5-tuple of set, binary operations on this set (addition and multiplication), one unary operation (addition inverse) and one nullary operation (0). And the following axioms hold.
addition is associative and commutative
multiplication is associative
0 is the additive identity
1 is the multiplicative identity
a⋅ (b + c) = (a· b) + (a· c) for all a, b, c in R
(b + c) · a = (b· a) + (c· a) for all a, b, c in R