Publication: On S-comultiplication modules
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Date
2022-01-01
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Abstract
Let R be a commutative ring with 1 ̸= 0 and M be an R-module. Suppose that S ⊆ R is a multiplicatively closed set of R. Recently Sevim et al. in [19] introduced the notion of an S -prime submodule which is a generalization of a prime submodule and used them to characterize certain classes of rings/modules such as prime submodules, simple modules, torsion free modules, S -Noetherian modules and etc. Afterwards, in [2], Anderson et al. defined the concepts of S -multiplication modules and S -cyclic modules which are S -versions of multiplication and cyclic modules and extended many results on multiplication and cyclic modules to S -multiplication and S -cyclic modules. Here, in this article, we introduce and study S -comultiplication modules which are the dual notion of S -multiplication module. We also characterize certain classes of rings/modules such as comultiplication modules, S -second submodules, S -prime ideals and S -cyclic modules in terms of S -comultiplication modules. Moreover, we prove S -version of the dual Nakayama’s Lemma.
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Matematik, Değişmeli Halkalar ve Cebirler, Temel Bilimler, Mathematics, Commutative Rings and Algebras, Natural Sciences, Temel Bilimler (SCI), Doğa Bilimleri Genel, ÇOK DİSİPLİNLİ BİLİMLER, MATEMATİK, Natural Sciences (SCI), NATURAL SCIENCES, GENERAL, MATHEMATICS, MULTIDISCIPLINARY SCIENCES, Multidisciplinary, Discrete Mathematics and Combinatorics, Geometry and Topology, Logic, Physical Sciences
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Yıldız E., Tekir Ü., Koç S., "On S-comultiplication modules", Turkish Journal Of Mathematics, cilt.46, ss.1-13, 2022