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Divisibility classes are seldom closed under flat covers
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SYSNO ASEP 0494437 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Divisibility classes are seldom closed under flat covers Author(s) Hrbek, Michal (MU-W) SAI, ORCID, RID Source Title Journal of Pure and Applied Algebra. - : Elsevier - ISSN 0022-4049
Roč. 223, č. 3 (2019), s. 1258-1271Number of pages 14 s. Language eng - English Country NL - Netherlands Keywords tilting module ; flat cover ; divisible module Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000449246900023 EID SCOPUS 85048724068 DOI 10.1016/j.jpaa.2018.06.005 Annotation We show that the class of all divisible modules over an integral domain R is closed under flat covers if and only if R is almost perfect. Also, we show that if the class of all s-divisible modules, where s is a regular element of a commutative ring R, is closed under flat covers then the quotient ring R/sR satisfies some rather restrictive properties. The question is motivated by the recent classification of tilting classes over commutative rings. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2020 Electronic address http://dx.doi.org/10.1016/j.jpaa.2018.06.005
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