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On topological lattices and their applications to module theory

Title
On topological lattices and their applications to module theory
Type
Article in International Scientific Journal
Year
2016
Authors
Abuhlail, J
(Author)
Other
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Christian Lomp
(Author)
FCUP
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Journal
Vol. 15
Final page: 1650046
ISSN: 0219-4988
Publisher: World Scientific
Scientific classification
CORDIS: Physical sciences > Mathematics ; Physical sciences > Mathematics > Algebra
Other information
Authenticus ID: P-00K-5GZ
Abstract (EN): Yassemi's "second submodules" are dualized and properties of its spectrum are studied. This is done by moving the ring theoretical setting to a lattice theoretical one and by introducing the notion of a (strongly) topological lattice L = (L, Lambda, V) with respect to a proper subset X of L. We investigate and characterize (strongly) topological lattices in general in order to apply it to modules over associative unital rings. Given a non-zero left R-module M, we introduce and investigate the spectrum Spec(f) (M) of first submodules of M as a dual notion of Yassemi's second submodules. We topologize Spec(f) (M) and investigate the algebraic properties of M by passing to the topological properties of the associated space.
Language: English
Type (Professor's evaluation): Scientific
No. of pages: 21
Documents
File name Description Size
Abuhlail-Lomp_JAA_rev revised version of published paper 331.18 KB
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