ON FULLY IDEMPOTENT MODULES

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dc.contributor.authorTutuncu, Derya Keskin
dc.contributor.authorErtas, Nil Orhan
dc.contributor.authorTribak, Rachid
dc.contributor.authorSmith, Patrick F.
dc.date.accessioned2024-09-29T16:01:14Z
dc.date.available2024-09-29T16:01:14Z
dc.date.issued2011
dc.departmentKarabük Üniversitesien_US
dc.description.abstractA submodule N of a module M is idempotent if N = Hom (M,N)N. The module M is fully idempotent if every submodule of M is idempotent. We prove that over a commutative ring, cyclic idempotent submodules of any module are direct summands. Counterexamples are given to show that this result is not true in general. It is shown that over commutative Noetherian rings, the fully idempotent modules are precisely the semisimple modules. We also show that the commutative rings over which every module is fully idempotent are exactly the semisimple rings. Idempotent submodules of free modules are characterized.en_US
dc.identifier.doi10.1080/00927872.2010.489916
dc.identifier.endpage2722en_US
dc.identifier.issn0092-7872
dc.identifier.issue8en_US
dc.identifier.scopus2-s2.0-80051816904en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage2707en_US
dc.identifier.urihttps://doi.org/10.1080/00927872.2010.489916
dc.identifier.urihttps://hdl.handle.net/20.500.14619/5608
dc.identifier.volume39en_US
dc.identifier.wosWOS:000297044900004en_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.subjectFully idempotent moduleen_US
dc.subjectIdempotent submoduleen_US
dc.titleON FULLY IDEMPOTENT MODULESen_US
dc.typeArticleen_US

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