The dimension graph of a commutative ring

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dc.authorid0000-0001-7039-2095
dc.contributor.authorBabaei, S.
dc.contributor.authorSevim, E. Sengelen
dc.date.accessioned2026-04-04T18:55:39Z
dc.date.available2026-04-04T18:55:39Z
dc.date.issued2024
dc.departmentİstanbul Bilgi Üniversitesi
dc.description.abstractThis paper introduces a simple graph associated to a commutative ring. Nonzero ideals I and J of a commutative ring R are called Krull dimension-dependent whenever dimR/(I+J)=min{dimR/I,dimR/J} . Based on this, we introduce the dimension graph of R. We study and investigate this graph, and we determine all rings with disconnected dimension graph. Moreover, we introduce strongly Krull dimension-dependent ideals, and we examine these ideals using a subgraph of the dimension graph.
dc.description.sponsorshipWe would like to express our sincere gratitude to the referee for his (her) great effort in proofreading the manuscript and for the several comments. This paper is much improved for the suggestions and insights.
dc.identifier.doi10.1080/00927872.2024.2362931
dc.identifier.doi10.1080/00927872.2024.2362931
dc.identifier.endpage5014
dc.identifier.issn0092-7872
dc.identifier.issn1532-4125
dc.identifier.issue12
dc.identifier.scopus2-s2.0-85197604097
dc.identifier.scopusqualityQ3
dc.identifier.startpage5005
dc.identifier.urihttps://doi.org/10.1080/00927872.2024.2362931
dc.identifier.urihttps://hdl.handle.net/11411/10509
dc.identifier.volume52
dc.identifier.wosWOS:001259286000001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherTaylor & Francis Inc
dc.relation.ispartofCommunications in Algebra
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260402
dc.snmzKA_Scopus_20260402
dc.subjectDimension Graphs
dc.subjectKrull Dimension-Dependent Ideals
dc.subjectStrong Dimension Graphs
dc.titleThe dimension graph of a commutative ring
dc.typeArticle

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