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dc.contributor.advisorPusat, Dilek
dc.contributor.authorKalaycı, Tekgül
dc.date.accessioned2014-11-18T13:35:40Z
dc.date.available2014-11-18T13:35:40Z
dc.date.issued2014
dc.identifier.urihttp://hdl.handle.net/11147/4185
dc.descriptionThesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2014en_US
dc.descriptionIncludes bibliographical references (leaves: 42)en_US
dc.descriptionText in English; Abstract: Turkish and Englishen_US
dc.descriptionvii, 42 leavesen_US
dc.description.abstractIn this thesis, we give a survey of necessary and sufficient conditions on a group G and a ring R for the group ring RG to be semiperfect and perfect. A ring R is called semiperfect R/RadR is semisimple and idempotents of R/RadR can be lifted to R. It is given that if RG is semiperfect, so is R. Necessary conditions on G for RG to be semiperfect are also given for some special type of groups. For the sufficient conditions, several types of rings and groups are considered. If R is commutative and G is abelian, a complete characterization is given in terms of the polynomial ring R[X]. A ring R is called left (respectively, right) perfect if R/Rad R is semisimple and Rad R is left (respectively, right) T-nilpotent. Equivalently, a ring is called left (respectively, right) perfect if R satisfies the descending chain condition on principal right (respectively, left) ideals. By using these equivalent definitions of a perfect ring and results from group theory, a complete characterization of a perfect group ring RG is given in terms of R and G.en_US
dc.language.isoengen_US
dc.publisherIzmir Institute of Technologyen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subject.lcshRings (Algebra)en_US
dc.titleSemiperfect and perfect group ringsen_US
dc.title.alternativeYarı mükemmel ve mükemmel grup halkaları üzerineen_US
dc.typemasterThesisen_US
dc.contributor.authorIDTR58692en_US
dc.contributor.departmentIzmir Institute of Technology. Mathematicsen_US
dc.relation.publicationcategoryTezen_US


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