Volume 21, Issue 2 (9-2026)
IJMSI 2026, 21(2): 205-231 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Rincón-Mejía H A, Garrido-Jiménez O A. On σ-classes of modules with applications. IJMSI 2026; 21 (2) :205-231
URL: http://ijmsi.ir/article-1-2324-en.html
URL: http://ijmsi.ir/article-1-2324-en.html
Abstract:
In this paper we introduce some lattices of classes of left
R-module relative to a preradical sigma. These lattices are generaliza-
tions of the lattices R-TORS, R-tors, R-nat, R-conat, of torsion theo-
ries, hereditary torsion theories, natural classes and conatural classes,
respectively. We define the lattices σ-(R-TORS), σ-(R-tors), σ-(R-nat),
σ-(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 (σ-HH) condition, which we introduce. We also
present some results about σ-retractable rings, σ-Max rings extending
results about Mod-retractable rings and Max rings.
R-module relative to a preradical sigma. These lattices are generaliza-
tions of the lattices R-TORS, R-tors, R-nat, R-conat, of torsion theo-
ries, hereditary torsion theories, natural classes and conatural classes,
respectively. We define the lattices σ-(R-TORS), σ-(R-tors), σ-(R-nat),
σ-(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 (σ-HH) condition, which we introduce. We also
present some results about σ-retractable rings, σ-Max rings extending
results about Mod-retractable rings and Max rings.
Keywords: Preradical, Lattices of module classes, Left Mod-retractable ring, Left semiartinian ring, Left max ring.
Type of Study: Research paper |
Subject:
Special
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
