# Projective modules over semi-local rings

Let $R$ be a semi-local ring, and $M$ a finite projective $R$-module. If the localizations $M_m$ have the same rank for all maximal ideals $m$ of $R$ then $M$ is free.

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Is it Noetherian? –  Harry Gindi Jan 25 '11 at 1:26
Also, this sounds like homework. I'm voting to close based on the fact that there is technically no question here, just a statement. –  Harry Gindi Jan 25 '11 at 1:28
Hey, I only need help. However it is not Noetherian. –  John Jan 25 '11 at 2:51
This would be better asked at math.stackexchange.com, since it is not a research level question, and will surely be closed soon. –  Emerton Jan 25 '11 at 4:31
For a proof in the commutative case see math.stackexchange.com/questions/150944/… –  user26857 Jan 27 '13 at 10:36