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

作　　者：Toma ALBU Mihai IOSIF 

机构地区：[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

出　　处：《Frontiers of Mathematics in China》2016年第4期815-828,共14页中国高等学校学术文摘·数学（英文）

摘　　要：In this paper, which is a continuation 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 （Cll） or （C12）. Applications are given to Grothendieck categories and module categories equipped with hereditary torsion theories.In this paper, which is a continuation 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 （Cll） or （C12）. Applications are given to Grothendieck categories and module categories equipped with hereditary torsion theories.

关 键 词：Modular complement lattice C12 theory element LATTICE upper closed element LATTICE Goldie dimension continuous lattice essential element uniform lattice condition （Ci） Cll socle Grothendieck category torsion 

分 类 号：O571.413[理学—粒子物理与原子核物理] O344.3[理学—物理]