The conditions (C-i) in modular lattices, and applications

ALBU T., IOSIF M., TERCAN A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.15, no.1, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1142/s0219498816500018
  • Title of Journal : JOURNAL OF ALGEBRA AND ITS APPLICATIONS

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.