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dc.contributor.advisorOman, Greg G.
dc.contributor.authorHarmon, Luke Everett
dc.contributor.committeememberAbrams, Gene
dc.contributor.committeememberMesyan, Zachary
dc.contributor.committeememberMalmskog, Beth
dc.contributor.committeememberMorrow, Greg
dc.date.accessioned2020-06-01T10:00:58Z
dc.date.available2020-06-01T10:00:58Z
dc.date.submitted2020-05
dc.descriptionIncludes bibliographical references.
dc.description.abstractA bounded partially ordered set (P, 0, 1, ≤) is lower finite provided P is infinite and for each x 6= 1 in P, there are but finitely many elements y in Psuch that y < x. We will call a module M lower finite if the set of proper submodules of M, partially ordered by set-theoretic containment, is lower finite. We will use the(well-studied) class of Jonsson modules (along with other classical results) to classify the lower finite modules over a commutative ring with identity.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierHarmon_uccs_0892D_10544.pdf
dc.identifier.urihttps://hdl.handle.net/10976/167279
dc.languageEnglish
dc.publisherUniversity of Colorado Colorado Springs. Kraemer Family Library
dc.relation.ispartofDissertations
dc.rightsCopyright of the original work is retained by the author.
dc.subjectCommutative
dc.subjectLattice
dc.subjectRing
dc.subjectJonsson
dc.subjectAlgebra
dc.subjectModule
dc.titleLower Finite Modules Over Commutative Rings With Identity
dc.typeText
dcterms.cdm.subcollectionMathematics
thesis.degree.disciplineCollege of Letters, Arts, and Sciences-Mathematics
thesis.degree.grantorUniversity of Colorado Colorado Springs
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)


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