On lattices associated to rings with respect to a preradical

Year 2022, Volume: 31 Issue: 31, 13 - 37, 17.01.2022

Erwin Cerda-leon Hugo Rıncon-mejıa

https://doi.org/10.24330/ieja.1058385

Abstract

We introduce some new lattices of classes of modules with respect to appropriate preradicals. We introduce some concepts associated with these
lattices, such as the $\sigma$-semiartinian rings, the $\sigma$-retractable modules, the $\sigma$-$V$-rings, the $\sigma$-max rings. We continue to study $\sigma$-torsion theories, $\sigma$-open classes, $\sigma$-stable classes. We prove some theorems that extend some known results. Our results fall into well known situations when the preradical $\sigma$ is chosen as the identity preradical.

Keywords

Preradical, lattice of module class, hereditary torsion class, boolean lattice, V-ring, max-ring

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