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Idempotent Submodules

Title
Idempotent Submodules
Type
Technical Report
Year
2006
Authors
Christian Lomp
(Author)
FCUP
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Scientific classification
FOS: Natural sciences > Mathematics
CORDIS: Physical sciences > Mathematics > Algebra
Other information
Resumo (PT): 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 theories can 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.
Abstract (EN): 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 theories can 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.
Language: English
Type (Professor's evaluation): Scientific
Reference: CMUP 2006-38
No. of pages: 7
License type: Click to view license CC BY-NC
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idempotent Technical Report 141.78 KB
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