The conditions (Ci) in modular lattices, and applications
2015 ◽
Vol 15
(01)
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pp. 1650001
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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.
2004 ◽
Vol 03
(04)
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pp. 391-410
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1996 ◽
Vol 120
(1)
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pp. 87-101
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Keyword(s):
2007 ◽
Vol 307
(2)
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pp. 841-863
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Keyword(s):
2003 ◽
Vol 99
(2)
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pp. 361-372
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1987 ◽
Vol 101
(2)
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pp. 221-231
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Keyword(s):
1967 ◽
Vol 63
(3)
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pp. 647-652
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Keyword(s):