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Dec 10, 2022 at 10:35 comment added Jeremy Rickard @theL Although it may not technically be Nakayama's lemma, it's still true for finite dimensional algebras that if $M\otimes_AA/\operatorname{rad}A=0$ then $M=0$, even if $M$ is not finitely generated.
Nov 23, 2022 at 20:00 comment added the L @MarianoSuárez-Álvarez can you really use Nakayama? the modules here are not finitely generated.
Jun 11, 2022 at 10:04 history edited David White CC BY-SA 4.0
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May 30, 2022 at 23:16 comment added Mariano Suárez-Álvarez It is slightly simpler to just take a minimal resolution of M and tensor it with A/radA: the differentials of the resulting complex are all zero, and the modules nonzero because of Nakayama.
May 30, 2022 at 17:44 vote accept Reading finitisitic
May 30, 2022 at 17:37 history answered Mare CC BY-SA 4.0