Spring 2023 CHARACTERIZING S-PROJECTIVE MODULES AND S-SEMISIMPLE RINGS BY UNIFORMITY
Xiaolei Zhang, Wei Qi
J. Commut. Algebra 15(1): 139-149 (Spring 2023). DOI: 10.1216/jca.2023.15.139

Abstract

Let R be a ring and S a multiplicative subset of R. An R-module P is called uniformly S-projective provided that the induced sequence 0HomR(P,A)HomR(P,B)HomR(P,C)0 is u-S-exact for any u-S-short exact sequence 0ABC0. Some characterizations and properties of u-S-projective modules are obtained. The notion of u-S-semisimple modules is also introduced. A ring R is called a u-S-semisimple ring provided that any free R-module is u-S-semisimple. Several characterizations of u-S-semisimple rings are provided in terms of u-S-semisimple modules, u-S-projective modules, u-S-injective modules and u-S-split u-S-exact sequences.

Citation

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Xiaolei Zhang. Wei Qi. "CHARACTERIZING S-PROJECTIVE MODULES AND S-SEMISIMPLE RINGS BY UNIFORMITY." J. Commut. Algebra 15 (1) 139 - 149, Spring 2023. https://doi.org/10.1216/jca.2023.15.139

Information

Received: 27 January 2022; Revised: 13 July 2022; Accepted: 17 July 2022; Published: Spring 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604792
zbMATH: 07725181
Digital Object Identifier: 10.1216/jca.2023.15.139

Subjects:
Primary: 16D40
Secondary: 16D60

Keywords: u-S-injective module , u-S-projective module , u-S-semisimple ring , u-S-split u-S-exact sequence

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.15 • No. 1 • Spring 2023
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