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

Revision as of 01:55, 22 December 2019

Revision as of 01:57, 22 December 2019

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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 subtleties like a distinction between free and projective modules are concerned. This is really not surprising if you remember algebraic topology: stable problems and situations tend to be easy (or equivalently boring for mathematicians). But this type of a general discussion probably belongs to the main article "[[projective module]]". -- [[User:TakuyaMurata|Taku]] ([[User talk:TakuyaMurata|talk]]) 01:54, 22 December 2019 (UTC)