The conditions (Ci) in modular lattices, and applications-Reference-Cited by-同舟云学术

The conditions (Ci) in modular lattices, and applications

Published:2015-09-07 Issue:01 Volume:15 Page:1650001
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Albu Toma¹,Iosif Mihai²,Tercan Adnan³

Affiliation:

1. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 5, P.O. Box 1 – 764, RO – 010145 Bucharest 1, Romania

2. Department of Mathematics, Bucharest University, Academiei Str. 14, RO – 010014 Bucharest 1, Romania

3. Department of Mathematics, Hacettepe University, Beytepe Campus 06532 Ankara, Turkey

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498816500018

Reference11 articles.

1. The Osofsky–Smith Theorem for Modular Lattices and Applications (I)

2. The Osofsky-Smith Theorem for Modular Lattices, and Applications (II)

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