Generalizations Of Second Submodules

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dc.authoridkoç, suat/0000-0003-1622-786X
dc.authorwosidkoç, suat/AAI-5671-2021
dc.contributor.authorGezen, Secil Ceken
dc.contributor.authorTekir, Unsal
dc.contributor.authorKoc, Suat
dc.contributor.authorKelleqi, Ajlin
dc.date.accessioned2024-06-12T11:13:58Z
dc.date.available2024-06-12T11:13:58Z
dc.date.issued2020
dc.departmentTrakya Üniversitesien_US
dc.description.abstractIn this paper, we introduce and study some new generalizations of second submodules via a function phi on the set of all submodules of a module. Let R be a ring with non-zero identity, M be an R-module and phi : S(M) -> S(M) be a function where S(M) is the set of all submodules of M. A non-zero submodule N of M is said to be a phi-second submodule if, for any element a of R and a submodule K of M, aN subset of K and a phi(N) not subset of K imply either N subset of K or a is an element of ann(R)(N). Let n >= 2 be an integer and phi(n) : S(M) -> S(M) be the function defined by phi(n)(L) = (L : (M) ann(R)(L)(n-1)) for every L is an element of S(M). Then a phi(n)-second submodule of M is said to be an n-almost second submodule of M. We determine various algebraic properties of these submodules and investigate their relationships with other known submodule classes such as second, prime and semisimple submodules. We study the structure of n-almost second submodules of modules over ZPI-rings and Dedekind domains. We also give some characterizations of modules and submodules by using n-almost second submodules.en_US
dc.identifier.doi10.2298/FIL2012995C
dc.identifier.endpage4004en_US
dc.identifier.issn0354-5180
dc.identifier.issue12en_US
dc.identifier.scopus2-s2.0-85100742937en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage3995en_US
dc.identifier.urihttps://doi.org/10.2298/FIL2012995C
dc.identifier.urihttps://hdl.handle.net/20.500.14551/23753
dc.identifier.volume34en_US
dc.identifier.wosWOS:000616962900009en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherUniv Nis, Fac Sci Mathen_US
dc.relation.ispartofFilomaten_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectSecond Submoduleen_US
dc.subjectPhi-Second Submoduleen_US
dc.subjectN-Almost Second Submoduleen_US
dc.subjectAlmost Second Submoduleen_US
dc.subjectDual Notionen_US
dc.subjectPrimeen_US
dc.subjectModulesen_US
dc.titleGeneralizations Of Second Submodulesen_US
dc.typeArticleen_US

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