ARTINIAN \(\ bf{M}\)-COMPLETE ASSOCIATIVE RINGS

In 1996, the first author defined analogs of the concepts of complete (divisible), reduced, and periodic abelian groups, well-known in the theory of abelian groups, for arbitrary varieties of algebras. In 2021, the first author proposed a modification of the concepts of completeness and reducibility...

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Bibliographic Details
Published inUral mathematical journal Vol. 10; no. 1
Main Authors Leonid M. Martynov, Tatiana V. Pavlova
Format Journal Article
LanguageEnglish
Published Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin 01.07.2024
Subjects
associative ring, artinian ring, finite ring, complete ring, reduced ring
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Summary:In 1996, the first author defined analogs of the concepts of complete (divisible), reduced, and periodic abelian groups, well-known in the theory of abelian groups, for arbitrary varieties of algebras. In 2021, the first author proposed a modification of the concepts of completeness and reducibility, which is more natural in the case of associative rings. The paper studies the modification of these concepts for associative rings. Artinian \(\mathbf{M}\)-complete, \(\mathbf{M}\)-reduced rings, and minimally \(\mathbf{M}\)-complete associative nilpotent rings, simple rings with unity, and finite rings are characterized.
ISSN:2414-3952
DOI:10.15826/umj.2024.1.008