Person: KOÇ, SUAT
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KOÇ
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SUAT
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Publication Open Access On modules satisfying s-noetherian spectrum condition(2022-03-01) KOÇ, SUAT; TEKİR, ÜNSAL; Özen M., Naji O. A., Tekir Ü., Koç S.Let R be a commutative ring having nonzero identity and M be a unital R-module. Assume that S ⊆ R is a multiplicatively closed subset of R. Then, M satisfies SNoetherian spectrum condition if for each submodule N of M, there exist s ∈ S and a finitely generated submodule F ⊆ N such that sN ⊆ radM (F), where radM (F) is the prime radical of F in the sense (McCasland and Moore in Commun Algebra 19(5):1327–1341, 1991). Besides giving many properties and characterizations of SNoetherian spectrum condition, we prove an analogous result to Cohen’s theorem for modules satisfying S-Noetherian spectrum condition. Moreover, we characterize modules having Noetherian spectrum in terms of modules satisfying the S-Noetherian spectrum condition.Publication Metadata only Locally torsion-free modules(2022-01-01) TEKİR, ÜNSAL; KOÇ, SUAT; Jayaram C., Uǧurlu E. A., TEKİR Ü., KOÇ S.© 2023 World Scientific Publishing Company.Recall that a commutative ring R is a locally integral domain if its localization RP is an integral domain for each prime ideal P of R. Our aim in this paper is to extend the notion of locally integral domains to modules. Let R be a commutative ring with a unity and M a nonzero unital R-module. M is called a locally torsion-free module if the localization MP of M is a torsion-free RP-module for each prime ideal P of R. In addition to giving many properties of locally torsion-free modules, we use them to characterize Baer modules, torsion free modules, and von Neumann regular rings.