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Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics]
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Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics], 2024, Issue 1, Pages 84–93
DOI: https://doi.org/10.26456/vtpmk704 (Mi vtpmk704) 		 
Mathematical Logic, Algebra, Number Theory and Discrete Mathematics

On Artinian and Noeterian modules relative to a torsion theory and ACC/DCC on essential submodules

A. M. Chernev

MPEI, Moscow
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DOI: https://doi.org/10.26456/vtpmk704
Abstract: The paper concern on the properties of Artinian and Noeterian modules relative to a torsion theory. It is shown that ACC (resp. DCC) on essential submodules equivalents that a module is Artinian (resp. Noeterian), for modules with finite Goldie dimension. It is shown that ACC (resp. DCC) on essential closed submodules equivalents factor on relative socle is Artinian (resp. Noeterian).
Keywords: torsion theory, Artinian module, Noeterian module, socle of module relative to a torsion theory.
Received: 30.08.2023
Revised: 12.12.2023
Bibliographic databases:
Document Type: Article
UDC: 512.553.1
MSC: 16S90
Language: Russian
Citation: A. M. Chernev, “On Artinian and Noeterian modules relative to a torsion theory and ACC/DCC on essential submodules”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2024, no. 1, 84–93
Citation in format AMSBIB
\Bibitem{Che24}
\by A.~M.~Chernev
\paper On Artinian and Noeterian modules relative to a torsion theory and ACC/DCC on essential submodules
\jour Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]
\yr 2024
\issue 1
\pages 84--93
\mathnet{http://mi.mathnet.ru/vtpmk704}
\crossref{https://doi.org/10.26456/vtpmk704}
\elib{https://elibrary.ru/item.asp?id=65645559}
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