Factor ring of a ring

  • Thread starter tinynerdi
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  • #1
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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.
 

Answers and Replies

  • #2
Dick
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ZxZ/5Z doesn't even make much sense. 5Z isn't a subring of ZxZ.
 
  • #3
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I forgot about that.. let try Z/ZxZ =~ Z Since ZxZ is a subring of Z.
 
  • #4
Dick
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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.
 

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