Prove the set of integers is a commutative ring with identity


by Square1
Tags: commutative, identity, integers, prove, ring
Square1
Square1 is offline
#1
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?
Phys.Org News Partner Science news on Phys.org
Review: With Galaxy S5, Samsung proves less can be more
Making graphene in your kitchen
Study casts doubt on climate benefit of biofuels from corn residue
micromass
micromass is online now
#2
Nov10-12, 03:19 PM
Mentor
micromass's Avatar
P: 16,645
We can't answer this. You need to ask your professor whether you can just cite these facts without explicitly showing them.
Square1
Square1 is offline
#3
Nov10-12, 03:22 PM
P: 115
I had that feeling haha. Thanks.


Register to reply

Related Discussions
How to prove that pZ is a maximal ideal for the ring of integers? Linear & Abstract Algebra 25
"a≡b mod n" true in ring of algebraic integers => true in ring of integers Linear & Abstract Algebra 4
non commutative ring Linear & Abstract Algebra 2
non-commutative ring Calculus & Beyond Homework 0