Finiteness of a non-commutative ring

1. Apr 24, 2010

xixi

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. Apr 24, 2010

zhentil

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...

3. Apr 25, 2010

xixi

so then??...

4. Apr 26, 2010

Landau

then RxF is an infinite non-commutative ring...
so....

5. Apr 26, 2010

xixi

Do you mean that RxF is a counter-example ? but RxF has infinite non-unit elements .

6. Apr 26, 2010

zhentil

Silly me! I should read the question.