Yayınlanmış 1 Ocak 2016 | Sürüm v1
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The conditions (C-i) in modular lattices, and applications

  • 1. Acad Romana, Simion Stoilow Inst Math, Res Unit 5, RO-010145 Bucharest 1, Romania
  • 2. Univ Bucharest, Dept Math, RO-010014 Bucharest 1, Romania
  • 3. Hacettepe Univ, Dept Math, TR-06532 Ankara, Turkey

Açıklama

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.

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