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

Toma ALBU; Mihai IOSIF

doi:10.1007/s11464-016-0550-y

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Front. Math. China ›› 2016, Vol. 11 ›› Issue (4) : 815-828. DOI: 10.1007/s11464-016-0550-y

RESEARCH ARTICLE

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

Toma ALBU¹ ,
Mihai IOSIF²

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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

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Toma ALBU, Mihai IOSIF. New results on C₁₁ and C₁₂ lattices with applications to Grothendieck categories and torsion theories. Front. Math. China, 2016, 11(4): 815‒828 https://doi.org/10.1007/s11464-016-0550-y

References

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