Not sure exactly what you mean. But I try anyway.Originally Posted by earlkaize
Consider the integral domain, , regocnize that it is a commutative ring with unity (by definition) therefore you can speak of ideals. Note that for any , that the coset is an ideal in . Form a factor ring, . And you end with,
Note, all the intergers are divided among these cosets. Further, since cosets are equivalence classes they are all disjoint! Proof complete.
The ring formed by these cosets behaves just like the number under addition modulo , in fact, it is a famous result that you should memorize that,