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equivalence relation

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Prove that the equivalence relation modulo m where m is an integer, forms a ring.

Also, does this same equivalence relation form a field and why?

For this proof, you are given that [a]m (m is a subscript) represents an equivalence class modulo m, where m is an integer. We also know that for any two integers, a and b, that
[a]m + [b]m = [a + b]m and
[a]m[b]m = [ab]m

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Solution Preview

Proof:
We know the element in has the form , the element in has the form , the element in has the form , the element in has ...

Solution Summary

This post evaluates an equivalence relation.

$2.19