ON THE NOTION OF STRONG IRREDUCIBILITY AND ITS DUAL

• Type: Article in International Scientific Journal
• Date: 2013

Authors

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

Journal

Title: Journal of Algebra and its Applications

ISSN: 0219-4988

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 6 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-004-ZQ8

DOI: 10.1142/S0219498813500126

Abstract (EN): This note gives a unifying characterization and exposition of strongly irreducible elements and their duals in lattices. The interest in the study of strong irreducibility stems from commutative ring theory, while the dual concept of strong irreducibility had been used to define Zariski-like topologies on specific lattices of submodules of a given module over an associative ring. Based on our lattice theoretical approach, we give a unifying treatment of strong irreducibility, dualize results on strongly irreducible submodules, examine its behavior under central localization and apply our theory to the frame of hereditary torsion theories.

Language: English

Type (Professor's evaluation): Scientific