On \(\sigma\)-classes of modules with applications

In this paper we introduce some lattices of classes of left R-module relative to a preradical sigma. These lattices are generalizations of the lattices R-TORS, R-tors, R-nat, R-conat, of torsion theories, hereditary torsion theories, natural classes and conatural classes, respectively. We define the...

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: Garrido-Jiménez, Oscar A, Rincón-Mejía, Hugo A
Format: Article
Language:English
Subjects:
Lattices
Modules
Online Access:Get full text
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Summary:In this paper we introduce some lattices of classes of left R-module relative to a preradical sigma. These lattices are generalizations of the lattices R-TORS, R-tors, R-nat, R-conat, of torsion theories, hereditary torsion theories, natural classes and conatural classes, respectively. We define the lattices \(\sigma\)-(R-TORS), \(\sigma\)-(R-tors), \(\sigma\)-(R-nat), \(\sigma\)-(R-conat), which reduce to the lattices mentioned above, when one takes sigma as the identity. We characterize the equality between these lattices by means of the (\(\sigma\)-HH) condition, which we introduce. We also present some results about \(\sigma\)-retractable rings, \(\sigma\)-Max rings extending results about Mod-retractable rings and Max rings.
ISSN:2331-8422