On the Annihilator Submodules and the Annihilator Essential Graph

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dc.authoridSengelen Sevim, Esra/0000-0003-1296-0845
dc.contributor.authorBabaei, Sakineh
dc.contributor.authorPayrovi, Shiroyeh
dc.contributor.authorSevim, Esra Sengelen
dc.date.accessioned2024-07-18T20:42:24Z
dc.date.available2024-07-18T20:42:24Z
dc.date.issued2019
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractLet R be a commutative ring and let M be an R-module. For a is an element of R, Ann(M)(a) = {m is an element of M : am = 0} is said to be an annihilator submodule of M. In this paper, we study the property of being prime or essential for annihilator submodules of M. Also, we introduce the annihilator essential graph of equivalence classes of zero divisors of M, AE(R)(M), which is constructed from classes of zero divisors, determined by annihilator submodules of M and distinct vertices [a] and [b] are adjacent whenever Ann(M)(a) + Ann(M)(b) is an essential submodule of M. Among other things, we determine when AE(R)(M) is a connected graph, a star graph, or a complete graph. We compare the clique number of AE(R)(M) and the cardinal of m -Ass(R)(M).en_US
dc.identifier.doi10.1007/s40306-018-00306-1
dc.identifier.endpage914en_US
dc.identifier.issn0251-4184
dc.identifier.issn2315-4144
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85072979234en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage905en_US
dc.identifier.urihttps://doi.org/10.1007/s40306-018-00306-1
dc.identifier.urihttps://hdl.handle.net/11411/7269
dc.identifier.volume44en_US
dc.identifier.wosWOS:000486035200005en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringer Singapore Pte Ltden_US
dc.relation.ispartofActa Mathematica Vietnamicaen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectAnnihilator Submoduleen_US
dc.subjectAnnihilator Essential Graphen_US
dc.subjectZero Divisor Graphen_US
dc.subjectZero-Divisor Graphen_US
dc.titleOn the Annihilator Submodules and the Annihilator Essential Graphen_US
dc.typeArticleen_US

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