Publication:
Dual krull dimension and quotient finite dimensionality

dc.contributor.coauthorIosif, Mihai
dc.contributor.coauthorTeply, Mark L.
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorAlbu, Toma
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T23:50:32Z
dc.date.issued2005
dc.description.abstractA 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.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue1
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.volume284
dc.identifier.doi10.1016/j.jalgebra.2004.09.024
dc.identifier.issn0021-8693
dc.identifier.quartileQ2
dc.identifier.scopus2-s2.0-12144255120
dc.identifier.urihttps://doi.org/10.1016/j.jalgebra.2004.09.024
dc.identifier.urihttps://hdl.handle.net/20.500.14288/14560
dc.identifier.wos226588200004
dc.keywordsUpper continuous lattice
dc.keywordsKrull dimension
dc.keywordsDual krull dimension
dc.keywordsSubdirectly
dc.keywordsIrreducible
dc.keywordsMeet irreducible
dc.keywordsGoldie dimension
dc.keywordsQfd lattice
dc.keywordsGrothendieck category
dc.keywordsTorsion theory hopkıns-levitzki theorem
dc.keywordsModular lattices
dc.keywordsDeviation
dc.keywordsLocalization
dc.keywordsSets
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofJournal of Algebra
dc.subjectMathematics
dc.titleDual krull dimension and quotient finite dimensionality
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorAlbu, Toma
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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