On torsion theories and open classes of linear modular lattices

Abstract

AbstractGiven a ring R, a bijection exists between torsion theories and idempotent radicals. Further, the class of hereditary torsion theories contains the skeleton of the open classes. In this work, we extend the notions and main results in R-Mod about torsion classes, torsion-free classes, and open classes to the category LM of linear lattices, whose objects are complete modular lattices and whose morphisms are linear morphisms.KEYWORDS: Big latticescomplete modular latticesidempotent lattice preradicallattice preradicallinear morphism of latticesopen classesradicaltorsion theoriesTTF classes2020 MATHEMATICS SUBJECT CLASSIFICATION: Primary: 18B35Secondary: 06C9906B75 AcknowledgmentThe authors thank the referee for his precise and accurate suggestions and comments, which allowed them to enhance this work.Notes1 We say that a torsion theory is hereditary if and only if its torsion class is hereditary.

Locations

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