# Zero divisor polynomial [duplicate]

Let $f(x)\in R[x]$ be a zero divisor. How to prove that there is an element $0\neq a\in R$ such that $af(x) = 0$?

If $R$ has no nilpotent elements, it is easy. What about the general case? Can anyone help me? Thanks.

• Thanks for the comment. I know it is true as N.Jacobson has noted in his book: Basi Algebra, Vol I. – ksj03 Jul 10 '13 at 4:17
• I have tracked down Bill's answer: math.stackexchange.com/a/83171/11763 (Also, $R$ is commutative in your question right? If so, you should state so.) – anon Jul 10 '13 at 4:18
• Thanks very much. Please close this question. – ksj03 Jul 10 '13 at 5:05