Year: 2025
Type: article
Abstract: A left and right noetherian semiperfect ring R is known to be indecomposable if and only if its factor by the second power of Jacobson radical is. This characterization is used to study simple R-modules in terms of their Ext groups. It is shown that if R is indecomposable, all its simple modules are either finite or have the same infinite cardinality and their endomorphism rings have the same characteristics. The results are further strengthened in the case when R is quasi-Frobenius.
Author: Dominik Krasula
Institution: Charles University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407122741