On modules and rings in which complements are isomorphic to direct summands

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dc.authoridTaşdemir, Özgür/0000-0003-2500-8255
dc.authorwosidTaşdemir, Özgür/B-3626-2019
dc.contributor.authorKarabacak, Fatih
dc.contributor.authorKosan, M. Tamer
dc.contributor.authorQuynh, T. Cong
dc.contributor.authorTasdemir, Ozgur
dc.date.accessioned2024-06-12T10:58:03Z
dc.date.available2024-06-12T10:58:03Z
dc.date.issued2022
dc.departmentTrakya Üniversitesien_US
dc.description.abstractA right R-module M is virtually extending (or CIS) if every complement submodule of M is isomorphic to a direct summand of M, and M is called a virtually C2-module if every complement submodule of M which is isomorphic to a direct summand of M is itself a direct summand. The class of virtually extending modules (respectively, virtually C2-modules) is a strict and simultaneous generalization of extending modules (respectively, unifies extending modules and C2-modules): M is a semisimple module if and only if M is virtually semisimple and C2, and M is an extending module if and only if M is virtually extending and virtually C2. Furthermore, every virtually simple right R-module is injective if and only if R is a right V-ring and the class of virtually simple right R-modules coincides with the class of simple right R-modules. Among other results, we show that (1) if all cyclic sub-factors of a cyclic weakly co-Hopfian right R-module M are virtually extending, then M is a finite direct sum of uniform submodules; (2) every distributive virtually extending module over any Noetherian ring is a direct sum of uniform submodules; (3) over a right Noetherian ring, every virtually extending module satisfies the Schroder-Bernstein property; (4) being virtually extending (VC2) is a Morita invariant property; (4) if M circle plus E(M) is a VC2-module where E(-) denotes the injective hull, then M is injective.en_US
dc.identifier.doi10.1080/00927872.2021.1979026
dc.identifier.endpage1168en_US
dc.identifier.issn0092-7872
dc.identifier.issn1532-4125
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85117469464en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage1154en_US
dc.identifier.urihttps://doi.org/10.1080/00927872.2021.1979026
dc.identifier.urihttps://hdl.handle.net/20.500.14551/19916
dc.identifier.volume50en_US
dc.identifier.wosWOS:000709735700001en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherTaylor & Francis Incen_US
dc.relation.ispartofCommunications In Algebraen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectCo-Hopfian Moduleen_US
dc.subjectOsofsky-Smith Theoremen_US
dc.subjectSchroder-Bernstein Propertyen_US
dc.subjectSquare-Free Moduleen_US
dc.subjectVirtually Extending Moduleen_US
dc.subjectVirtually C2 Moduleen_US
dc.subjectVirtually Semisimple Moduleen_US
dc.subjectSubmodulesen_US
dc.subjectPropertyen_US
dc.titleOn modules and rings in which complements are isomorphic to direct summandsen_US
dc.typeArticleen_US

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