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


ALBU T., IOSIF M., TERCAN A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.15, sa.1, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 15 Konu: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s0219498816500018
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Özet

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.