Register to reply 
Prove the set of integers is a commutative ring with identity 
Share this thread: 
#1
Nov1012, 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? 


#2
Nov1012, 03:19 PM

Mentor
P: 18,278

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



#3
Nov1012, 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  
Noncommutative ring  Calculus & Beyond Homework  0 