Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/10298
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dc.contributor.authorÜngör, Burcu-
dc.contributor.authorKafkas, Gizem-
dc.contributor.authorHalıcıoğlu, Sait-
dc.contributor.authorHarmancı, Abdullah-
dc.date.accessioned2021-01-24T18:33:39Z-
dc.date.available2021-01-24T18:33:39Z-
dc.date.issued2012-
dc.identifier.issn1303-5991-
dc.identifier.issn2618-6470-
dc.identifier.urihttps://hdl.handle.net/11147/10298-
dc.identifier.urihttps://doi.org/10.1501/Commua1_0000000675-
dc.description.abstractR birimli bir halka, M saº g R-mod¸l ve M nin endomorÖzma halkas¨ S = EndR(M) olsun. Her f 2 S iÁin rM(f) = eM olacak biÁimde e2 = e 2 S varsa (denk olarakKerf,Mmod¸l¸n¸nbirdirekttoplanan¨ise)MyeRickartmod¸lad¨verilmi?stir[8]. BuÁal¨?smadaRickartmod¸llerinˆzellikleriincelenmeyedevamedilmi?stir. M birRickart mod¸l olmak ¸zere, M nin S-kat¨ (s¨ras¨yla S-indirgenmi?s, S-simetrik, S-yar¨ deºgi?smeli, S-Armendariz)mod¸l olmas¨ iÁin gerek ve yeter ?sart¨n S nin kat¨ (s¨ras¨yla indirgenmi?s, simetrik, yar¨ deºgi?smeli, Armendariz) halka olduºgu gˆsterilmi?stir. M[x], S[x] halkas¨na gˆre Rickart mod¸l iken M nin de Rickart mod¸l oldugu,tersinin M nin S-Armendariz olmas¨ durumunda doºgru olduºgu ispatlanm¨?st¨r. Ayrıca bir M mod¸l¸n¸n Rickart ol- mas¨iÁingerekveyeter?sart¨nhersaºgmod¸l¸nM-temelprojektifolduºgueldeedilmi?stir.en_US
dc.description.abstractLet Rbeanarbitraryringwithidentity and M aright R-module with S =EndR(M). Following [8],the module M is called Rickart if for any f 2 S, rM(f) = eM for some e2 = e 2 S, equivalently, Kerf is a direct summandofM. Inthispaper,wecontinuetoinvestigatepropertiesofRickart modules. For a Rickart module M, we prove that M is S-rigid (resp., S- reduced, S-symmetric, S-semicommutative, S-Armendariz) if and only if its endomorphism ring S is rigid (resp., reduced, symmetric, semicommutative, Armendariz). We also prove that if M[x]is a Rickart module with respect to S[x], then M is Rickart, the converse holds if M is S-Armendariz. Among others it is also shown that M is a Rickart module if and only if every right R-module is M-principally projective.en_US
dc.language.isoenen_US
dc.publisherAnkara Üniversitesien_US
dc.relation.ispartofCommunications Series A1: Mathematics and Statisticsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectSymmetric modulesen_US
dc.subjectRickart modulesen_US
dc.subjectReduced modulesen_US
dc.titleSome Properties of Rickart Modulesen_US
dc.typeArticleen_US
dc.institutionauthorKafkas, Gizemtr
dc.departmentİzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume61en_US
dc.identifier.issue2en_US
dc.identifier.startpage1en_US
dc.identifier.endpage8en_US
dc.relation.publicationcategoryMakale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanıtr
dc.identifier.trdizinid180152en_US
item.grantfulltextopen-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.cerifentitytypePublications-
item.languageiso639-1en-
item.fulltextWith Fulltext-
Appears in Collections:Mathematics / Matematik
TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection
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