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Jul 11, 2016 at 23:36 comment added roy smith this proof is given in one sentance on page 1 of Serre's Local Algebra.
Jan 12, 2013 at 10:50 comment added ACL Do you have a published reference for this proof?
Jan 12, 2013 at 10:50 comment added ACL By the way, if you're ready to zornicate/zornify, rather observe that the set of proper submodules of a non-zero finitely generated module is inductive, hence has a maximal element.
Jan 12, 2013 at 10:49 comment added ACL +1 for the Zornication!
Apr 27, 2011 at 21:29 comment added user1421 That's the way I like to think of it too: a finitely generated module over any ring (with identity) has a simple quotient.
Apr 13, 2011 at 8:25 history edited user91132 CC BY-SA 3.0
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Apr 13, 2011 at 8:14 history answered user91132 CC BY-SA 3.0