Finiteness of a non-commutative ring

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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?
 
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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...
 
zhentil said:
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...

so then??...
 
then RxF is an infinite non-commutative ring...
so...
 
Landau said:
then RxF is an infinite non-commutative ring...
so...

Do you mean that RxF is a counter-example ? but RxF has infinite non-unit elements .
 
Silly me! I should read the question.
 

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