Factor Ring of a Ring: Example of Integral Domain with Divisors of 0

[tinynerdi]

Homework Statement

give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain.

Homework Equations

since we know that ZxZ is a zero divisor and 5Z is an integral domain.

The Attempt at a Solution

So, ZxZ/5Z =~(isomorphic to) Z/5Z=~ Z_5.

 

[Dick]

ZxZ/5Z doesn't even make much sense. 5Z isn't a subring of ZxZ.

 

[tinynerdi]

I forgot about that.. let try Z/ZxZ =~ Z Since ZxZ is a subring of Z.

 

[Dick]

I forgot about that.. let try Z/ZxZ =~ Z Since ZxZ is a subring of Z.

How are you considering ZxZ as a subring of Z? ZxZ is ordered pairs of integers, isn't it? Z is just integers.