Publication: Dual krull dimension and quotient finite dimensionality
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Iosif, Mihai
Teply, Mark L.
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Abstract
A modular lattice L with 0 and 1 is called quotient finite dimensional (QFD) if [x, 1] has no infinite independent set for any x epsilon L. We characterize upper continuous modular lattices L that have dual Krull dimension k(0) (L) less than or equal to alpha, by relating that with the property of L being QFD and with other conditions involving subdirectly irreducible lattices and/or meet irreducible elements. In particular, we answer in the positive, in the more general latticial setting, some open questions on QFD modules raised by Albu and Rizvi [Comm. Algebra 29 (2001) 1909-1928]. Applications of these results are given to Grothendieck categories and module categories equipped with a torsion theory. (C) 2004 Elsevier Inc. All rights reserved.
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Publisher
Elsevier
Subject
Mathematics
Citation
Has Part
Source
Journal of Algebra
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Edition
DOI
10.1016/j.jalgebra.2004.09.024