On rings admitting nonzero homomorphisms between non-projective modules

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dc.authoridalagoz, yusuf/0000-0002-2535-4679
dc.authoridDURGUN, YILMAZ/0000-0002-1230-8964
dc.contributor.authorAlagoz, Yusuf
dc.contributor.authorDurgun, Yilmaz
dc.contributor.authorIzci, Kemal
dc.date.accessioned2024-12-24T19:28:02Z
dc.date.available2024-12-24T19:28:02Z
dc.date.issued2023
dc.departmentSiirt Üniversitesi
dc.description.abstractIn a recent paper, Turkoglu have studied the rings admitting nonzero homomorphisms between any two non-projective modules (property (T)). His work raises the following question: What are the rings with nonzero maps between non-projective right modules and singular simple modules? As a generalization of the property (T), we consider two families of rings: those rings with nonzero maps from any non-projective module to any singular simple module (property (T1)) and those rings with nonzero maps from any singular simple module to any non-projective module (property (T2)). Complete characterizations of both classes of rings are obtained and it is shown, in particular, that the rings satisfying property (T) are precisely those rings satisfying both properties (T1) and (T2). We show that R satisfies (T) if and only if R has a unique singular simple right R-module, and R is either two-sided Artinian hereditary serial or right completely coretractable. Furthermore, we prove that a commutative ring R has the property (T) if and only if there is a ring decomposition R approximately equal to AxB , where A is semisimple Artinian and B satisfies one of the following conditions: (1) B is a semi-Artinian max ring with unique singular simple right R-module. (2) B is an Artinian hereditary serial ring with unique singular simple right R-module.
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TUBITAK) [119F176]
dc.description.sponsorshipThis work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) (Project number: 119F176).
dc.identifier.doi10.1080/00927872.2022.2139972
dc.identifier.endpage1622
dc.identifier.issn0092-7872
dc.identifier.issn1532-4125
dc.identifier.issue4
dc.identifier.scopus2-s2.0-85142152926
dc.identifier.scopusqualityQ2
dc.identifier.startpage1614
dc.identifier.urihttps://doi.org/10.1080/00927872.2022.2139972
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6894
dc.identifier.volume51
dc.identifier.wosWOS:000882858800001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherTaylor & Francis Inc
dc.relation.ispartofCommunications in Algebra
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241222
dc.subjectProjective modules
dc.subject(semi-)Artininan rings
dc.subjectsingular simple modules
dc.titleOn rings admitting nonzero homomorphisms between non-projective modules
dc.typeArticle

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