Pseudocomplements and strong pseudocomplements in lattices of module classes

Alvarado-García, Alejandro; Cejudo-Castilla, César; Rincón-Mejía, Hugo Alberto; Vilchis-Montalvo, Ivan Fernando

doi:10.1142/s0219498818500160

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Preradicals and Lattices Of Module Classes1

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2019

2021

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Cited by 4 publications

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“…We refer to [1][2][3][4]9], for basic results about hereditary, cohereditary, natural, conatural and open classes.…”

Section: Preradicals and Lattices Of Module Classesmentioning

confidence: 99%

Big lattices of module classes induced by preradicals

Cerda-León

Rincón-Mejía

2019

São Paulo J. Math. Sci.

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We introduce new big lattices of classes of R-modules induced by suitable preradicals, the big lattice of σ-hereditary classes, the big lattice of σ-cohereditary classes, and the big lattice of σ-open classes. We prove that their Skeletons are boolean lattices which generalize and extend the lattice of natural classes, the lattice of conatural classes and the Skeleton of the lattice of hereditary torsion theories, respectively. We also introduce the lattice of σ-hereditary torsion theories, for a exact preradical σ. In case that σ be the identity preradical, we obtain the usual lattice of hereditary torsion classes.

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“…We refer to [1][2][3][4]9], for basic results about hereditary, cohereditary, natural, conatural and open classes.…”

Section: Preradicals and Lattices Of Module Classesmentioning

confidence: 99%