Divisibility classes are seldom closed under flat covers

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00494437" target="_blank" >RIV/67985840:_____/19:00494437 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1016/j.jpaa.2018.06.005" target="_blank" >http://dx.doi.org/10.1016/j.jpaa.2018.06.005</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2018.06.005" target="_blank" >10.1016/j.jpaa.2018.06.005</a>

Result language

angličtina

Original language name

Divisibility classes are seldom closed under flat covers

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

—

Volume of the periodical

223

Issue of the periodical within the volume

3

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

14

Pages from-to

1258-1271

UT code for WoS article

000449246900023

EID of the result in the Scopus database

2-s2.0-85048724068