Flat commutative ring epimorphisms of almost Krull dimension zero

0569842 - MÚ 2024 RIV SG eng J - Článek v odborném periodiku
Positselski, Leonid
Flat commutative ring epimorphisms of almost Krull dimension zero.
Journal of Algebra and its Applications. Roč. 22, č. 3 (2023), č. článku 2350060. ISSN 0219-4988. E-ISSN 1793-6829
Grant CEP: GA ČR(CZ) GA20-13778S
Institucionální podpora: RVO:67985840
Klíčová slova: semilocal commutative rings of Krull dimension zero * contramodules * Gabriel filters of ideals in commutative rings
Obor OECD: Pure mathematics
Impakt faktor: 0.8, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1142/S0219498823500603

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.
Trvalý link: https://hdl.handle.net/11104/0341173