Prove the set of integers is a commutative ring with identity

by Square1
Tags: commutative, identity, integers, prove, ring
Square1 is offline
Nov10-12, 03:08 PM
P: 115
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?
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micromass is offline
Nov10-12, 03:19 PM
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P: 16,703
We can't answer this. You need to ask your professor whether you can just cite these facts without explicitly showing them.
Square1 is offline
Nov10-12, 03:22 PM
P: 115
I had that feeling haha. Thanks.

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