Talk:Kaplansky's theorem on projective modules: Difference between revisions

Revision as of 10:36, 19 December 2019

Revision as of 02:44, 20 December 2019

Line 4:

:The assumption on “local” is needed in the second lemma; I’m preparing the proof and so this should be fixed. (What is crucial is on the behavior of indecomposable decompositions not local; “local” is used to make modules indecomposable, and the discussion of this crucial point is currently missing.) As for the second point, on theorem articles, sometimes what is interesting is the proof (here, for instance the use of countably generated modules) rather than the applications. I personally don’t know interesting applications since often one works with finitely generated projective modules. In this article, I think the focus should be on the proof, which involves many ideas that are of independent interest. —— [[User:TakuyaMurata|Taku]] ([[User talk:TakuyaMurata|talk]]) 09:37, 19 December 2019 (UTC)

:I have added a quote explaining the significance. If you know any applications, I’m interested to know. — [[User:TakuyaMurata|Taku]] ([[User talk:TakuyaMurata|talk]]) 09:51, 19 December 2019 (UTC)

:I have also added the formulation of the theorem that characterizes a local ring (this should also address the first comment). -- [[User:TakuyaMurata|Taku]] ([[User talk:TakuyaMurata|talk]]) 02:44, 20 December 2019 (UTC)