Abstract algebra: Rings and Ideals

  • Thread starter lmedin02
  • Start date
  • #1
56
0

Homework Statement


The problem is to show that a subset A of a ring S is an ideal where A has certain properties. S is a ring described as a cartisian product of two other rings (i.e., S=(RxZ,+,*)). I have already proved that A is a subring of S and proved one direction of the definition of an ideal. But, the other direction has brought me to having to show that R is commutative. It is given that R is a ring without zero divisors and without identity.


Homework Equations





The Attempt at a Solution


I know that a ring R is commutative if it has the property that ab=ca implies b=c when a is not zero. I have attempted various simple manipulations of this statement by using the fact that R is a ring without zero divisors and without an identity.
 

Answers and Replies

  • #2
56
0
In other words, is a ring R without zero divisors and without an identity commutative.
 
  • #4
56
0
An integral domain has a unity (i.e., identity). In my case, R has no unity so it is not an integral domain.
 

Related Threads on Abstract algebra: Rings and Ideals

  • Last Post
Replies
3
Views
6K
  • Last Post
Replies
3
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
0
Views
2K
Replies
5
Views
3K
Replies
2
Views
3K
Replies
1
Views
2K
Top