(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let R be a ring that contains at least two elements. Suppose for each nonzero a in R, there exists a unique b in R such that aba=a.

Show that R has no divisors of 0.

2. Relevant equations

3. The attempt at a solution

Let a*c=0 where a,c are not equal to 0.

aba=a implies aba-a=0=nac where n is any integer which implies that a(ba-1-nc)=0

I am not seeing the contradiction.

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# Homework Help: Ring theory problem

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