Flat ring epimorphisms of countable type
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00523855" target="_blank" >RIV/67985840:_____/20:00523855 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/S001708951900017X" target="_blank" >https://doi.org/10.1017/S001708951900017X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S001708951900017X" target="_blank" >10.1017/S001708951900017X</a>
Alternative languages
Result language
angličtina
Original language name
Flat ring epimorphisms of countable type
Original language description
Let R → U be an associative ring epimorphism such that U is a flat left R-module. Assume that the related Gabriel topology of right ideals in R has a countable base. Then we show that the left R-module U has projective dimension at most 1. Furthermore, the abelian category of left contramodules over the completion of R at fully faithfully embeds into the Geigle-Lenzing right perpendicular subcategory to U in the category of left R-modules, and every object of the latter abelian category is an extension of two objects of the former one. We discuss conditions under which the two abelian categories are equivalent. Given a right linear topology on an associative ring R, we consider the induced topology on every left R-module and, for a perfect Gabriel topology, compare the completion of a module with an appropriate Ext module. Finally, we characterize the U-strongly flat left R-modules by the two conditions of left positive-degree Ext-orthogonality to all left U-modules and all -separated -complete left R-modules.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - 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
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Glasgow Mathematical Journal
ISSN
0017-0895
e-ISSN
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Volume of the periodical
62
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
57
Pages from-to
383-439
UT code for WoS article
000525379300008
EID of the result in the Scopus database
2-s2.0-85065401417