Countably generated module

id: countably-generated-module-261-11264298
title: Countably generated module
text: In mathematics, a module over a ring is countably generated if it is generated as a module by a countable subset. The importance of the notion comes from Kaplansky's theorem, which states that a projective module is a direct sum of countably generated modules. More generally, a module over a possibly non-commutative ring is projective if and only if (i) it is flat, (ii) it is a direct sum of countably generated modules and (iii) it is a Mittag-Leffler module. (Bazzoni–Stovicek)
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category slug: encyclopedia
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original url: https://en.wikipedia.org/wiki/Countably_generated_module
date created:
date modified: 2023-08-12T18:54:33Z
main entity: {"identifier":"Q5176825","url":"https://www.wikidata.org/entity/Q5176825"}
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integrity: 13

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