1. The conditions (Ci) in modular lattices, and applications.
- Author
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Albu, Toma, Iosif, Mihai, and Tercan, Adnan
- Subjects
- *
MODULAR lattices , *MODULES (Algebra) , *LATTICE theory , *CUBIC crystal system , *GROTHENDIECK categories , *TORSION theory (Algebra) - Abstract
In this paper, we introduce and investigate the latticial counterparts of the conditions (Ci), i = 1, 2, 3, 11, 12, for modules. In particular, we study the lattices satisfying the condition (C1), 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. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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