Number of the records: 1
Flat commutative ring epimorphisms of almost Krull dimension zero
- 1.0569842 - MÚ 2024 RIV SG eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GA20-13778S
Institutional support: RVO:67985840
Keywords : semilocal commutative rings of Krull dimension zero * contramodules * Gabriel filters of ideals in commutative rings
OECD category: Pure mathematics
Impact factor: 0.8, year: 2022
Method of publishing: Limited access
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.
Permanent Link: https://hdl.handle.net/11104/0341173
File Download Size Commentary Version Access Positselski1.pdf 1 318.2 KB Publisher’s postprint require
Number of the records: 1