Weak u-S-flat Modules and Dimensions
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In this paper, we generalize the notions uniformly S-flat, briefly u-S-flat, modules and dimensions. We introduce and study the notions of weak u-S-flat modules. An R-module M is said to be weak u-S-flat if TorR 1 (R/I, M) is u-S-torsion for any ideal I of R. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the weak u-S-flat dimensions of modules and rings. The rela tions between the introduced dimensions and other (classical) homological dimensions are discussed.
Abstract
In this paper, we generalize the notions uniformly S-flat, briefly u-S-flat, modules and dimensions. We introduce and study the notions of weak u-S-flat modules. An R-module M is said to be weak u-S-flat if TorR 1 (R/I, M) is u-S-torsion for any ideal I of R. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the weak u-S-flat dimensions of modules and rings. The rela tions between the introduced dimensions and other (classical) homological dimensions are discussed.
참고문헌 (5)
- S. Glaz, "Commutative coherent rings" (1989), Springer
- F. Wang, "Foundations of Commutative Rings and Their Modules" (2016), Springer Nature Singapore Pte Ltd
- Xiaolei Zhang, "Characterizing $S$-flat modules and $S$-von Neumann regular rings by uniformity", 대한수학회보, 59(3), pp.643~657 (2022), 대한수학회[DOI]
- "u-S-absolutely pure modules"[URL]
- Xiaolei Zhang, "The $u$-$S$-weak global dimensions of commutative rings", 대한수학회논문집, 38(1), pp.97~112 (2023), 대한수학회[DOI]