Divisibility classes are seldom closed under flat covers

0494437 - MÚ 2020 RIV NL eng J - Journal Article
Hrbek, Michal
Divisibility classes are seldom closed under flat covers.
Journal of Pure and Applied Algebra. Roč. 223, č. 3 (2019), s. 1258-1271. ISSN 0022-4049. E-ISSN 1873-1376
Institutional support: RVO:67985840
Keywords : tilting module * flat cover * divisible module
OECD category: Pure mathematics
Impact factor: 0.770, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.jpaa.2018.06.005

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.
Permanent Link: http://hdl.handle.net/11104/0287624