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Finiteness of a non-commutative ring

  1. Apr 24, 2010 #1
    Let R be a non-commutative ring . Suppose that the number of non-units of R is finite . Can we say that R is a finite ring?
     
  2. jcsd
  3. Apr 24, 2010 #2
    If R and F are rings, then RxF is a ring. In particular, if R is a finite non-commutative ring and F is a field...
     
  4. Apr 25, 2010 #3
    so then??...
     
  5. Apr 26, 2010 #4

    Landau

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    then RxF is an infinite non-commutative ring...
    so....
     
  6. Apr 26, 2010 #5
    Do you mean that RxF is a counter-example ? but RxF has infinite non-unit elements .
     
  7. Apr 26, 2010 #6
    Silly me! I should read the question.
     
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