Originally Posted by

**jenjen** I also found this defintion

Def: A ring (with identity) is a set R with two operations, addition and mutiplication, and two special elements, 0 and 1, which satisfy axioms (associativity of addition, communtativity of addition, 0 is a zero element, etc.). The operations addition and multiplication may each be thought of as functions from R x R (ordered pairs of elements of the set R) to R, so that for any ordered pair (a,b), where a, b are in R, a + b is an element of R, and a x b is an element of R.