On lattices associated to rings with respect to a preradical

Authors : Erwin CERDALEON, Hugo RINCONMEJIA

Pages : 13-37

Doi:10.24330/ieja.1058385

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Publication Date : 2022-01-17

Article Type : Research Paper

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