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

Revision as of 09:51, 19 December 2019

Revision as of 09:55, 19 December 2019

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I have two comments: the proof of the theorem in the article currently does not highlight the point where the assumption that the ring is local is used. This could be improved. Secondly, [[WP:NOTTEXTBOOK|WP is not a textbook]], and this article is practically an excerpt of a textbook. I think the article would gain much from rather highlighting applications of the theorem and also from [[WP:WE|not addressing the reader directly]]. [[User:Jakob.scholbach|Jakob.scholbach]] ([[User talk:Jakob.scholbach|talk]]) 08:23, 19 December 2019 (UTC)

: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, and 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 thethis article, I think the focus of this article should be on the proof, which involveinvolves 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)