MODULES AND THE SECOND CLASSICAL ZARISKI TOPOLOGY

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dc.authorwosidAlkan, Mustafa/C-1981-2016
dc.contributor.authorCeken, Secil
dc.contributor.authorAlkan, Mustafa
dc.date.accessioned2024-06-12T11:13:58Z
dc.date.available2024-06-12T11:13:58Z
dc.date.issued2018
dc.departmentTrakya Üniversitesien_US
dc.description.abstractLet R be an associative ring with identity and Spec(s)(M) denote the set of all second submodules of a right R-module M. In this paper, we present a number of new results for the second classical Zariski topology on Spec(s)(M) for a right R-module M. We obtain a characterization of semisimple modules by using the second spectrum of a module. We prove that if R is a ring such that every right primitive factor of R is right artinian, then every non-zero submodule of a second right R-module M is second if and only if M is a fully prime module. We give some equivalent conditions for Spec(s)(M) to be a Hausdorff space or T-i-space when the right R-module M has certain algebraic properties. We obtain characterizations of commutative Quasi-Frobenius and artinian rings by using topological properties of the second classical Zariski topology. We give a full characterization of the irreducible components of Spec(s)(M) for a non-zero injective right module M over a ring R such that every prime factor of R is right or left Goldie.en_US
dc.description.sponsorshipScientific Research Project Administration of Akdeniz Universityen_US
dc.description.sponsorshipThe second author was supported by the Scientific Research Project Administration of Akdeniz University.en_US
dc.identifier.doi10.4418/2018.73.1.12
dc.identifier.endpage177en_US
dc.identifier.issn0373-3505
dc.identifier.issn2037-5298
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85048186328en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage161en_US
dc.identifier.urihttps://doi.org/10.4418/2018.73.1.12
dc.identifier.urihttps://hdl.handle.net/20.500.14551/23754
dc.identifier.volume73en_US
dc.identifier.wosWOS:000434633200012en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherUniv Studi Catania, Dipt Matematicaen_US
dc.relation.ispartofMatematicheen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectSecond Submoduleen_US
dc.subjectSecond Spectrumen_US
dc.subjectPrime Submoduleen_US
dc.subjectSecond Classical Zariski Topologyen_US
dc.subjectNoncommutative Ringsen_US
dc.subjectPrime Spectrumen_US
dc.subjectDual Notionen_US
dc.subjectSubmodulesen_US
dc.titleMODULES AND THE SECOND CLASSICAL ZARISKI TOPOLOGYen_US
dc.typeArticleen_US

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