Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/2945
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dc.contributor.advisorBüyükaşık, Enginen
dc.contributor.authorDemirci, Yılmaz Mehmet-
dc.date.accessioned2014-07-22T13:48:39Z-
dc.date.available2014-07-22T13:48:39Z-
dc.date.issued2012en
dc.identifier.urihttp://hdl.handle.net/11147/2945-
dc.descriptionThesis (Doctoral)-Izmir Institute of Technology, Mathematics, Izmir, 2012en
dc.descriptionIncludes bibliographical references (leaves: 55-57)en
dc.descriptionText in English; Abstract: Turkish and Englishen
dc.descriptionix, 57 leavesen
dc.descriptionFull text release delayed at author's request until 2015.12.03en
dc.description.abstractThe purpose of this study is to understand the properties of the operations +, ◦, and * defined on classes of short exact sequences and apply them to the proper classes related to supplements. The operation ◦ on classes of short exact sequences is introduced and it is proved that the class of extended weak supplements is the result of the operation ◦ applied to two classes one of which is the class of splitting short exact sequences. Using the direct sum of proper classes defined by R. Alizade, G. Bilhan and A. Pancar, a direct sum decomposition for quasi-splitting short exact sequences over the ring of integers is obtained. Closures of classes of short exact sequences along with the one studied by C. P. Walker, N. Hart and R. Alizade are defined over an integral domain. It is shown that these classes are proper when the underlying class is proper and they are related to the operation +. The closures of proper classes related to supplements are described in terms of Ivanov classes. Closures for modules over an integral domain are also defined and it is proved that submodules of torsion-free modules have unique closures. A closure for classes of short exact sequences is defined over an associative ring with identity and it is proved that this closure is proper when the underlying class is proper. Results shows that the operation + and closures of splitting short exact sequences plays an important role on the closures of proper classes.en
dc.language.isoenen_US
dc.publisherIzmir Institute of Technologyen
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subject.lcshAlgebra, Homologicalen
dc.subject.lcshModules (Algebra)en
dc.titleOperations on proper classes related to supplementsen_US
dc.typeDoctoral Thesisen_US
dc.institutionauthorDemirci, Yılmaz Mehmet-
dc.departmentIzmir Institute of Technology. Mathematicsen_US
dc.relation.publicationcategoryTezen_US
item.openairetypeDoctoral Thesis-
item.languageiso639-1en-
item.fulltextWith Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.cerifentitytypePublications-
item.grantfulltextopen-
Appears in Collections:Phd Degree / Doktora
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