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KOÇ, SUAT

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KOÇ

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SUAT

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2016 - 20194
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End date: 2019 × Start date: 2016 ×

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Now showing 1 - 4 of 4
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    On n-absorbing delta-primary ideals
    (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2018) KOÇ, SUAT; Ulucak, Gulsen; Tekir, Unsal; Koc, Suat
    Let R be a commutative ring with nonzero identity and n be a positive integer. In this paper, we study the concepts of n-absorbing delta-primary ideals and weakly n-absorbing delta-primary ideals, which are the generalizations of delta-primary ideals and weakly delta-primary ideals, respectively. We introduce the concepts of n-absorbing delta-primary ideals and weakly n-absorbing delta-primary ideals. Moreover, we give many properties of these new types of ideals and investigate the relations between these structures.
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    On S-prime submodules
    (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2019) KOÇ, SUAT; Sengelen Sevim, Esra; Arabaci, Tarik; Tekir, Unsal; Koc, Suat
    In this study, we introduce the concepts of S-prime submodules and S-torsion-free modules, which are generalizations of prime submodules and torsion-free modules. Suppose S subset of R is a multiplicatively closed subset of a commutative ring R, and let M be a unital R-module. A submodule P of M with (P : (R) M) boolean AND S = empty set is called an S-prime submodule if there is an s is an element of S such that am is an element of P implies sa is an element of(P : (R) M) or sm is an element of P: Also, an R-module M is called S-torsion-free if ann(M) boolean AND S = empty set and there exists s is an element of S such that am = 0 implies sa = 0 or sm = 0 for each a is an element of R and m is an element of M: In addition to giving many properties of S-prime submodules, we characterize certain prime submodules in terms of S-prime submodules. Furthermore, using these concepts, we characterize some classical modules such as simple modules, S-Noetherian modules, and torsion-free modules.
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    r-Submodules and sr-Submodules
    (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2018) KOÇ, SUAT; Koc, Suat; Tekir, Unsal
    In this article, we introduce new classes of submodules called r-submodule and special r-submodule, which are two different generalizations of r-ideals. Let M be an R-module, where R is a commutative ring. We call a proper submodule N of M an r-submodule (resp., special r-submodule) if the condition am is an element of N with ann(M) (a) = 0(M) (resp., ann(R)(m) = 0) implies that m E N (resp., a is an element of (N :(R) M)) for each a is an element of R and m is an element of M. We also give various results and examples concerning r-submodules and special r-submodules.
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    On 2-Absorbing Quasi-Primary Ideals in Commutative Rings
    (SPRINGER HEIDELBERG, 2016) KOÇ, SUAT; Tekir, Unsal; Koc, Suat; Oral, Kursat Hakan; Shum, Kar Ping
    Let R be a commutative ring with nonzero identity. In this article, we introduce the notion of 2-absorbing quasi-primary ideal which is a generalization of quasi-primary ideal. We define a proper ideal I of R to be 2-absorbing quasi primary if root I is a 2-absorbing ideal of R. A number of results concerning 2-absorbing quasiprimary ideals and examples of 2-absorbing quasi-primary ideals are given.