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==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: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)
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::OK, these steps go in the right direction, I think -- thanks! I am by no means an expert on this topic, but searching around a bit reveals for example a paper by Bass " Big projective modules are free. " where he states it relies on Kaplansky's theorem. More systematically, it may also be instructive to check out the list of papers referring to Kaplansky's paper such as this [https://mathscinet.ams.org/mathscinet/search/publications.html?revcit=100017&loc=revcit list of papers whose MR review refers to Kaplansky's paper] is also insightful, I guess. [[User:Jakob.scholbach|Jakob.scholbach]] ([[User talk:Jakob.scholbach|talk]]) 08:27, 20 December 2019 (UTC)
:::Thank you for the info about Bass's result (which I didn't know). I have added it to the article. I think, while I understand the importance of mentioning applications in general, that this theorem (as well as Bass's result) says that big (=not finitely generated) modules are somehow ''boring'' as far as the
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