Geodesic
On Artinian and Noeterian modules relative to a torsion theory and ACC/DCC on essential submodules
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2024), pp. 84-93

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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. 
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     author = {A. M. Chernev},
     title = {On {Artinian} and {Noeterian} modules relative to a torsion theory and {ACC/DCC} on essential submodules},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {84--93},
     publisher = {mathdoc},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2024_1_a5/}
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A. M. Chernev. On Artinian and Noeterian modules relative to a torsion theory and ACC/DCC on essential submodules. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2024), pp. 84-93. http://geodesic.mathdoc.fr/item/VTPMK_2024_1_a5/