S-Artinian rings and finitely S-cogenerated rings

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dc.authoridkoç, suat/0000-0003-1622-786X|Sengelen Sevim, Esra/0000-0003-1296-0845
dc.authorwosidkoç, suat/AAI-5671-2021
dc.contributor.authorSevim, Esra Sengelen
dc.contributor.authorTekir, Unsal
dc.contributor.authorKoc, Suat
dc.date.accessioned2024-07-18T20:48:48Z
dc.date.available2024-07-18T20:48:48Z
dc.date.issued2020
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractLet R be a commutative ring with nonzero identity and S subset of R be a multiplicatively closed subset. In this paper, we study S-Artinian rings and finitely S-cogenerated rings. A commutative ring R is said to be an S-Artinian ring if for each descending chain of ideals {In}(n is an element of N) of R, there exist s is an element of S and k is an element of N such that sI(k) subset of I-n for all n >= k. Also, R is called a finitely S-cogenerated ring if for each family of ideals {I alpha}(alpha)(is an element of Delta) of R, = where Delta is an index set, boolean AND(alpha is an element of Delta) I alpha implies = 0 implies s(boolean AND(alpha is an element of Delta), I alpha) = 0 for some s is an element of S and a finite subset Delta' subset of Delta. Moreover, we characterize some special rings such as Artinian rings and finitely cogenerated rings. Also, we extend many properties of Artinian rings and finitely cogenerated rings to S-Artinian rings and finitely S-cogenerated rings.en_US
dc.identifier.doi10.1142/S0219498820500516
dc.identifier.issn0219-4988
dc.identifier.issn1793-6829
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85063188048en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1142/S0219498820500516
dc.identifier.urihttps://hdl.handle.net/11411/7930
dc.identifier.volume19en_US
dc.identifier.wosWOS:000525373900011en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherWorld Scientific Publ Co Pte Ltden_US
dc.relation.ispartofJournal of Algebra and Its Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectArtinian Ringen_US
dc.subjectFinitely Cogenerated Ringen_US
dc.subjectS-Artinian Ringen_US
dc.subjectFinitely S-Cogenerated Ringen_US
dc.subjectNoetherian Ringsen_US
dc.titleS-Artinian rings and finitely S-cogenerated rings
dc.typeArticle

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