- #1
ehrenfest
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Homework Statement
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.
Homework Equations
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.