The conditions (C-i) in modular lattices, and applications
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.15, no.1, 2016 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 15 Issue: 1
- Publication Date: 2016
- Doi Number: 10.1142/s0219498816500018
- Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Hacettepe University Affiliated: Yes
Abstract
In this paper, we introduce and investigate the latticial counterparts of the conditions (C-i), i = 1, 2, 3, 11, 12, for modules. In particular, we study the lattices satisfying the condition (C-1), we call CC lattices (for Closed are Complements), i.e. the lattices such that any closed element is a complement, that are the latticial counterparts of CS modules (for Closed are Summands). Applications of these results are given to Grothendieck categories and module categories equipped with a torsion theory.