DOI QR코드

DOI QR Code

CHARACTERIZING S-FLAT MODULES AND S-VON NEUMANN REGULAR RINGS BY UNIFORMITY

  • Zhang, Xiaolei (School of Mathematics and Statistics Shandong University of Technology)
  • 투고 : 2021.04.09
  • 심사 : 2022.01.24
  • 발행 : 2022.05.31

초록

Let R be a ring and S a multiplicative subset of R. An R-module T is called u-S-torsion (u-always abbreviates uniformly) provided that sT = 0 for some s ∈ S. The notion of u-S-exact sequences is also introduced from the viewpoint of uniformity. An R-module F is called u-S-flat provided that the induced sequence 0 → A ⊗R F → B ⊗R F → C ⊗R F → 0 is u-S-exact for any u-S-exact sequence 0 → A → B → C → 0. A ring R is called u-S-von Neumann regular provided there exists an element s ∈ S satisfying that for any a ∈ R there exists r ∈ R such that sα = rα2. We obtain that a ring R is a u-S-von Neumann regular ring if and only if any R-module is u-S-flat. Several properties of u-S-flat modules and u-S-von Neumann regular rings are obtained.

키워드

과제정보

The author was supported by the National Natural Science Foundation of China (No. 12061001).

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