Flat commutative ring epimorphisms of almost Krull dimension zero

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00569842" target="_blank" >RIV/67985840:_____/23:00569842 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1142/S0219498823500603" target="_blank" >https://doi.org/10.1142/S0219498823500603</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0219498823500603" target="_blank" >10.1142/S0219498823500603</a>

Result language
angličtina
Original language name
Flat commutative ring epimorphisms of almost Krull dimension zero
Original language description
In this paper, we consider flat epimorphisms of commutative rings R --> U such that, for every ideal I in R for which IU = U, the quotient ring R/I is semilocal of Krull dimension zero. Under these assumptions, we show that the projective dimension of the R-module U does not exceed 1. We also describe the Geigle-Lenzing perpendicular subcategory to the R-module U in R-Mod. Assuming additionally that the ring U and all the rings R/I are perfect, we show that all flat R-modules are U-strongly flat. Thus, we obtain a generalization of some results of a previous paper, where the case of the localization U of the ring R at a multiplicative subset S in R was considered.
Czech name
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Czech description
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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

Project
<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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