Publication: Modular QFD lattices with applications to grothendieck categories and torsion theories
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Co-Authors
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 is an element of L. We extend some results about QFD modules to upper continuous modular lattices by using Lemonnier's Lemma. One result says that QFD for a compactly generated lattice L is equivalent to Condition (C): for every m is an element of L, there exists a compact element t of L such that t is an element of [0, m] and [t, m[ has no maximal element. If L is not compactly generated, then QFD and (C) separate into two distinct conditions, which are analyzed and characterized for upper continuous modular lattices. We also extend to upper continuous modular lattices some characterizations of QFD modules with Gabriel dimension. Applications of these results are given to Grothendieck categories and module categories equipped with a torsion theory.
Source
Publisher
World Scientific Publishing
Subject
Applied, Mathematics
Citation
Has Part
Source
Journal of Algebra and Its Applications
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DOI
10.1142/S0219498804000939