Talk:Kaplansky's theorem on projective modules

Comments

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 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 not addressing the reader directly. Jakob.scholbach (talk) 08:23, 19 December 2019 (UTC)[reply]

The assumption on “local” is needed in the second lemma; I’m preparing the proof and so this should be fixed. 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 the article, I think the focus of this article should be on the proof, which involve many ideas that are of independent interest. —— Taku (talk) 09:37, 19 December 2019 (UTC)[reply]