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

doi:10.1007/s11464-016-0550-y

Front. Math. China

2016, Vol. 11

Issue (4) : 815-828 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 IOSIF²

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

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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 (C_i) 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.

Keywords Modular lattice upper continuous lattice essential element complement element closed element uniform lattice condition (C_i) C₁₁ lattice C₁₂ lattice Goldie dimension socle Grothendieck category torsion theory

Corresponding Author(s): Toma ALBU

Issue Date: 30 August 2016

Cite this article:

Toma ALBU,Mihai IOSIF. New results on C₁₁ and C₁₂ lattices with applications to Grothendieck categories and torsion theories[J]. Front. Math. China, 2016, 11(4): 815-828.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0550-y
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I4/815

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