On topological lattices and their applications to module theory

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Abuhlail, J (Author) Other; Christian Lomp (Author) FCUP

Journal

Title: Journal of Algebra and its Applications

Vol. 15

Final page: 1650046

ISSN: 0219-4988

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 6 Citations

Scientific classification

CORDIS: Physical sciences > Mathematics ; Physical sciences > Mathematics > Algebra

Other information

Authenticus ID: P-00K-5GZ

DOI: 10.1142/s0219498816500468

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