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 mingcai6172 April 29th, 2009 08:42 PM

finitely generated ideal, idempotent

Let $J$ be a finitely generated ideal such that $J=J^2$. Prove that $J$ is principal and generated by an idempotent.

This looks like a straightforward question, but I do not know how to prove this is principal or how this is generated by an idempotent. How should I go about showing this?

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