Some rings for which the cosingular submodule of every module is a direct summand

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dc.contributor.authorKeskin Tutuncu, Derya
dc.contributor.authorOrhan Ertas, Nil
dc.contributor.authorSmith, Patrick F.
dc.contributor.authorTribak, Rachid
dc.date.accessioned2024-09-29T16:08:20Z
dc.date.available2024-09-29T16:08:20Z
dc.date.issued2014
dc.departmentKarabük Üniversitesien_US
dc.description.abstractThe snbmodule (Z)overbar(M) = boolean AND{N vertical bar M/N is small in its injective hull} was introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P) if (Z)overbar(M) is a direct summand of M for every R-module M. It is shown that a commutative perfect ring R has (P) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M is an element of Mod-R vertical bar <(Z)overbar >(R)(M) = 0} is closed under factor modules, then R has (P) if and only if the ring R is von Neumann regular.en_US
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TUBITAK) [2221]en_US
dc.description.sponsorshipThis paper was written while the third author was visiting the Hacettepe University Mathematics Department in 2011. All authors wish to thank the Scientific and Technological Research Council of Turkey (TUBITAK) for financial support under the program 2221. We would also like to thank the referees for carefully reading this paper and for the numerous valuable comments on the paper.en_US
dc.identifier.doi10.3906/mat-1210-15
dc.identifier.endpage657en_US
dc.identifier.issn1300-0098
dc.identifier.issn1303-6149
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-84898965994en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage649en_US
dc.identifier.urihttps://doi.org/10.3906/mat-1210-15
dc.identifier.urihttps://hdl.handle.net/20.500.14619/7502
dc.identifier.volume38en_US
dc.identifier.wosWOS:000338003700004en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherTubitak Scientific & Technological Research Council Turkeyen_US
dc.relation.ispartofTurkish Journal of Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectvon Neumann regular ringen_US
dc.subjectperfect ringen_US
dc.subject(non)cosingular submoduleen_US
dc.titleSome rings for which the cosingular submodule of every module is a direct summanden_US
dc.typeArticleen_US

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