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Factor ring of a ring

  1. May 13, 2010 #1
    1. The problem statement, all variables and given/known data
    give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain.


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


    3. The attempt at a solution
    So, ZxZ/5Z =~(isomorphic to) Z/5Z=~ Z_5.
     
  2. jcsd
  3. May 13, 2010 #2

    Dick

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    ZxZ/5Z doesn't even make much sense. 5Z isn't a subring of ZxZ.
     
  4. May 14, 2010 #3
    I forgot about that.. let try Z/ZxZ =~ Z Since ZxZ is a subring of Z.
     
  5. May 14, 2010 #4

    Dick

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    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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