On minimal absolutely pure domain of RD-fllat modules

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dc.authoridalagoz, yusuf/0000-0002-2535-4679
dc.contributor.authorAlagoz, Yusuf
dc.date.accessioned2024-12-24T19:32:56Z
dc.date.available2024-12-24T19:32:56Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractGiven modules A(R) and B-R, B-R is called absolutely A(R)-pure if for every extension C-R of B-R, A circle times B -> A circle times C is a monomorphism. The class (Fl) under bar (-1)(A(R)) ={B-R : B-R is absolutely A(R)-pure} is called the absolutely pure domain of a module A(R). If B-R is divisible, then all short exact sequences starting with B is RD-pure, whence B is absolutey A-pure for every RD-flat module A(R). Thus the class of divisible modules is the smallest possible absolutely pure domain of an RD-flat module. In this paper, we consider RD-flat modules whose absolutely pure domains contain only divisible modules, and we referred to these RD-flat modules as rd-indigent. Properties of absolutely pure domains of RD-flat modules and of rd-indigent modules are studied. We prove that every ring has an rd-indigent module, and characterize rd-indigent abelian groups. Furthermore, over (commutative) SRDP rings, we give some characterizations of the rings whose nonprojective simple modules are rd-indigent.
dc.identifier.doi10.55730/1300-0098.3269
dc.identifier.endpage2303
dc.identifier.issn1300-0098
dc.identifier.issn1303-6149
dc.identifier.issue6
dc.identifier.scopus2-s2.0-85134370981
dc.identifier.scopusqualityQ2
dc.identifier.startpage2292
dc.identifier.trdizinid1142670
dc.identifier.urihttps://doi.org/10.55730/1300-0098.3269
dc.identifier.urihttps://search.trdizin.gov.tr/tr/yayin/detay/1142670
dc.identifier.urihttps://hdl.handle.net/20.500.12604/7891
dc.identifier.volume46
dc.identifier.wosWOS:000824597700017
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.indekslendigikaynakTR-Dizin
dc.language.isoen
dc.publisherTubitak Scientific & Technological Research Council Turkey
dc.relation.ispartofTurkish Journal of Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectRD-flat modules
dc.subjectabsolutely pure domains
dc.subjectrd-indigent modules
dc.subjectQF-rings
dc.titleOn minimal absolutely pure domain of RD-fllat modules
dc.typeArticle

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