Abstract
Let be a ring and a multiplicative subset of . An -module is called uniformly -projective provided that the induced sequence is --exact for any --short exact sequence . Some characterizations and properties of --projective modules are obtained. The notion of --semisimple modules is also introduced. A ring is called a --semisimple ring provided that any free -module is --semisimple. Several characterizations of --semisimple rings are provided in terms of --semisimple modules, --projective modules, --injective modules and --split --exact sequences.
Citation
Xiaolei Zhang. Wei Qi. "CHARACTERIZING -PROJECTIVE MODULES AND -SEMISIMPLE RINGS BY UNIFORMITY." J. Commut. Algebra 15 (1) 139 - 149, Spring 2023. https://doi.org/10.1216/jca.2023.15.139
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