Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493550 | Journal of Algebra | 2005 | 28 Pages |
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 xâL. We characterize upper continuous modular lattices L that have dual Krull dimension k0(L)⩽α, 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Toma Albu, Mihai Iosif, Mark L. Teply,