On the compressed essential graph of a commutative ring

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dc.contributor.authorPayrovi, Shiroyeh
dc.contributor.authorBabaei, Sakineh
dc.contributor.authorSevim, Esra Sengelen
dc.date.accessioned2024-07-18T20:50:42Z
dc.date.available2024-07-18T20:50:42Z
dc.date.issued2019
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractLet R be a commutative ring. In this paper, we introduce and study the compressed essential graph of R, EG(E)(R). The compressed essential graph of R is a graph whose vertices are equivalence classes of non-zero zero-divisors of R and two distinct vertices [x] and [y] are adjacent if and only if ann(xy) is an essential ideal of R. It is shown if R is reduced, then EG(E)(R) = Gamma(E)(R), where Gamma(E)(R) denotes the compressed zero-divisor graph of R. Furthermore, for a non-reduced Noetherian ring R with 3 < vertical bar EG(E)(R)vertical bar < infinity, it is shown that EG(E)(R) = Gamma(E)(R) if and only if (i) Nil(R) = ann(Z(R)). (ii) Every non-zero element of Nil(R) is irreducible in Z(R).en_US
dc.identifier.doi10.36045/bbms/1568685656
dc.identifier.endpage429en_US
dc.identifier.issn1370-1444
dc.identifier.issn2034-1970
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85074136107en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage421en_US
dc.identifier.urihttps://doi.org/10.36045/bbms/1568685656
dc.identifier.urihttps://hdl.handle.net/11411/8187
dc.identifier.volume26en_US
dc.identifier.wosWOS:000486383700007en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherBelgian Mathematical Soc Triompheen_US
dc.relation.ispartofBulletin of The Belgian Mathematical Society-Simon Stevinen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectEssential Graphen_US
dc.subjectZero Divisor Graphen_US
dc.subjectCompressed Zero-Divisor Graphen_US
dc.subject2-Absorbing İdealen_US
dc.subjectZero-Divisor Graphen_US
dc.titleOn the compressed essential graph of a commutative ring
dc.typeArticle

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