1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook