ABSTRACT
Section II in a Nutshell This section defines three important algebraic structures: rings, integral domains, and fields.
Well-known objects (Z, Q[x], Zm, Q, R, and C) share many algebraic properties. These properties define an abstract object called a ring :
A ring R is a set of elements on which two binary operations, addition (+) and multiplication (·), are defined that satisfy the following properties for all a, b, c ∈ R:
1. (Addition is commutative) a+ b = b+ a
2. (Addition is associative) (a+ b) + c = (a+ (b+ c)
3. (Additive identity exists) There exists an element 0 in R such that a+ 0 = a.
