Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 4: 815 - 828

DOI: https://doi.org/10.1007/s11464-016-0550-y

RESEARCH ARTICLE

New results on C11 and C12 lattices with applications to Grothendieck categories and torsion theories

  • Toma ALBU , 1 ,
  • Mihai IOSIF 2
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  • 1. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 5, P.O. Box 1-764, RO-010145 Bucharest 1, Romania
  • 2. Bucharest University, Department of Mathematics, Academiei Str. 14, RO-010014 Bucharest 1, Romania

Received date: 18 Oct 2015

Accepted date: 30 Nov 2015

Published date: 30 Aug 2016

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

In this paper, which is a cont inuation of our previous paper [T. Albu, M. Iosif, A. Tercan, The conditions (Ci) in modular lattices, and applications, J. Algebra Appl. 15 (2016), http: dx.doi.org/10.1142/S0219498816500018], we investigate the latticial counterparts of some results about modules satisfying the conditions (C11) or (C12). Applications are given to Grothendieck categories and module categories equipped with hereditary torsion theories.

Key words： Modular lattice; upper continuous lattice; essential element; complement element; closed element; uniform lattice; condition (Ci); C11 lattice; C12 lattice; Goldie dimension; socle; Grothendieck category; torsion theory

Cite this article

Toma ALBU , Mihai IOSIF . New results on C11 and C12 lattices with applications to Grothendieck categories and torsion theories[J]. Frontiers of Mathematics in China, 2016 , 11(4) : 815 -828 . DOI: 10.1007/s11464-016-0550-y

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