Not sure exactly what you mean. But I try anyway.Originally Posted byearlkaize

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,