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Very easy question about subring

  1. Feb 1, 2012 #1
    If the subring S of a ring R has a unit element e' but R does not have a unit element then e' must be a divisor of zero.

    I was able to show that if R has a unit element e≠e', then (e-e')e'=0, where e-e'≠0, implying e' is a divisor of zero, but if R does not have a unit element I can't see why, please help, thank you.
     
  2. jcsd
  3. Feb 1, 2012 #2

    Dick

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    If e' isn't a unit in R then there is an element of r of R such that e'r-r is not zero. Multiply that by e'.
     
    Last edited: Feb 1, 2012
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