Abstract
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.
| Original language | English |
|---|---|
| Article number | 1350012 |
| Journal | Journal of Algebra and its Applications |
| Volume | 12 |
| Issue number | 6 |
| DOIs | |
| State | Published - Sep 2013 |
Bibliographical note
Funding Information:The first author would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through project SB101023. Compiling this manuscript started during the visit of the second author to KFUPM. He would like to thank KFUPM for their hospitality. The second author was partially supported
Keywords
- Strongly irreducible ideals
- Zariski topology
- dual Zariski topology
- strongly hollow submodules
- strongly irreducible submodules
ASJC Scopus subject areas
- Algebra and Number Theory
- Applied Mathematics
Fingerprint
Dive into the research topics of 'On the notion of strong irreducibility and its dual'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver