Please use this identifier to cite or link to this item: https://hdl.handle.net/10216/25795
Author(s): Christian Lomp
Title: Idempotent Submodules
Issue Date: 2006
Abstract: Bican, Jambor, Kepka and Nemec defined a product on the lattice of submodules of a module, making any module into a partially ordered groupoid. Submodules that are idempotent with respect to this product behave similar as idempotent ideals in rings. In particular jansian torsion theoriescan be described through idempotent submodules. Moreover so-called coclosed submodules, which are essentially closed elements in the dual lattice of submodules of a module, turn out to be idempotent in pi-projective modules. The relation of strongly copolyform modules and the regularity of their endomorphism ring is discussed.
Description: Bican, Jambor, Kepka and Nemec defined a product on the lattice of submodules of a module, making any module into a partially ordered groupoid. Submodules that are idempotent with respect to this product behave similar as idempotent ideals in rings. In particular jansian torsion theoriescan be described through idempotent submodules. Moreover so-called coclosed submodules, which are essentially closed elements in the dual lattice of submodules of a module, turn out to be idempotent in pi-projective modules. The relation of strongly copolyform modules and the regularity of their endomorphism ring is discussed.
Subject: Álgebra, Matemática
Algebra, Mathematics
Scientific areas: Ciências exactas e naturais::Matemática
Natural sciences::Mathematics
URI: https://repositorio-aberto.up.pt/handle/10216/25795
Document Type: Relatório Técnico
Rights: openAccess
License: https://creativecommons.org/licenses/by-nc/4.0/
Appears in Collections:FCUP - Relatório Técnico

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