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Jun 14, 2017 at 12:48 comment added Jeremy Rickard @CountDracula Sorry, I read your comment just before I went to bed, and forgot to say thank you for pointing out my silly mistake.
Jun 14, 2017 at 10:09 history edited Jeremy Rickard CC BY-SA 3.0
added abelian group example
Jun 14, 2017 at 0:56 comment added Jian @JeremyRickard thank you!the answer is very clear and correct ,I'll try to understand finiteness condition.
Jun 14, 2017 at 0:55 vote accept Jian
Jun 13, 2017 at 21:53 history edited Jeremy Rickard CC BY-SA 3.0
deleted 232 characters in body
Jun 13, 2017 at 21:50 comment added Jeremy Rickard @CountDracula Quite right. But finitely generated flat modules over a local ring are projective, which is enough for a counterexample for a non-Noetherian ring. I'll correct it.
Jun 13, 2017 at 20:59 comment added Count Dracula It is not true that a flat module over a local ring is projective. Projective modules over local rings are free, but flat ones aren't... for example the rationals over the locazation of the integers at a prime.
Jun 13, 2017 at 16:09 history answered Jeremy Rickard CC BY-SA 3.0