# Prove the set of integers is a commutative ring with identity

1. Nov 10, 2012

### Square1

How should one prove that the integers form a commutative ring? Im not sure exactly where to go with this and how much should be explicitly shown.

A ring is meant to be a system that shares properties of Z and Zn. A commutative ring is a ring, with the commutative multiplication property. Only need to prove then that that the integers have a commutative multiplication property in that case?? But commutativity of multiplication is a known property of the set of integers, "an arithmetical fact" as my book says. So do I just cite this fact/theorem without having to show much algebra bingo bango its a com. ring? Same argument witht the identity elemnt. It is part of the list of arithmetic facts given to us, which themselves are not proven, so just cite it?

2. Nov 10, 2012

### micromass

Staff Emeritus
We can't answer this. You need to ask your professor whether you can just cite these facts without explicitly showing them.

3. Nov 10, 2012

### Square1

I had that feeling haha. Thanks.