Posner’s theorem and ∗-centralizing derivations on prime ideals with applications

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dc.authorid0000-0002-7874-2392en_US
dc.contributor.authorAli, Shakir
dc.contributor.authorAlsuraiheed, Turki M.
dc.contributor.authorKhan, Mohammad Salahuddin
dc.contributor.authorAbdioğlu, Cihat
dc.contributor.authorAyedh, Mohammed
dc.contributor.authorRafiquee, Naira N.
dc.date.accessioned2023-11-13T13:11:08Z
dc.date.available2023-11-13T13:11:08Z
dc.date.issued2023en_US
dc.departmentKMÜ, Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümüen_US
dc.descriptionWOS:001039706500001en_US
dc.description.abstractA well-known result of Posner's second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation are central, then the ring is commutative. In the present paper, we extended this bluestocking theorem to an arbitrary ring with involution involving prime ideals. Further, apart from proving several other interesting and exciting results, we established the *-version of Vukman's theorem. Precisely, we describe the structure of quotient ring U/L, where A is an arbitrary ring and L is a prime ideal of U. Further, by taking advantage of the *-version of Vukman's theorem, we show that if a 2-torsion free semiprime A with involution admits a nonzero *-centralizing derivation, then A contains a nonzero central ideal. This result is in the spirit of the classical result due to Bell and Martindale (Theorem 3). As the applications, we extended and unified several classical theorems. Finally, we conclude our paper with a direction for further research.en_US
dc.identifier.citationAli, S.; Alsuraiheed, T.M.; Khan, M.S.; Abdioglu, C.; Ayedh, M.; Rafiquee, N.N. (2023). Posner’s theorem and ∗-centralizing derivations on prime ideals with applications. Mathematics , 11(14). https:// doi.org/10.3390/math11143117en_US
dc.identifier.doi10.3390/math11143117
dc.identifier.issn2227-7390
dc.identifier.issue14en_US
dc.identifier.scopus2-s2.0-85175115833
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/math11143117
dc.identifier.urihttps://hdl.handle.net/11492/7701
dc.identifier.volume11en_US
dc.identifier.wosWOS:001039706500001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Sceince
dc.indekslendigikaynakScopus
dc.institutionauthorAbdioğlu, Cihat
dc.language.isoen
dc.publisherMDPIen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectDerivationen_US
dc.subject∗-Centralizing Derivationen_US
dc.subject∗-Commuting Derivationen_US
dc.subjectInvolutionen_US
dc.subjectPrime Idealen_US
dc.subjectPrime Ringen_US
dc.subjectSemiprime Ringen_US
dc.titlePosner’s theorem and ∗-centralizing derivations on prime ideals with applicationsen_US
dc.typeArticle

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