Question

How to prove the set of integers under addition and multiplication modulo n is a commutative ring with unity 1?​

Answer 1

A subring S of a ring R is a subset of R which is a ring under the same operations as R. A non-empty subset S of R is a subring if a, b ∈ S ⇒ a - b, ab ∈ S. So S is closed under subtraction and multiplication. Exercise: Prove that these two definitions are equivalent.

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