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    ON n-PRIME IDEALS
    (Univ Politehnica Bucharest, Sci Bull, 2018) Sevim, Esra Sengelen; Koc, Suat
    In this article, we introduce an intermediate classes of ideals between prime and quasi primary ideals, denoted by n-prime, and we focus on some properties of n-prime ideals. Moreover, we defined a topology on the set of all n-prime ideals such that we examine the topological concepts, irreducibility, connectedness, and seperation axioms.
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    On S-multiplication modules
    (Taylor & Francis Inc, 2020) Anderson, Dan D.; Arabaci, Tarik; Tekir, Unsal; Koc, Suat
    In this article, we introduce S-multiplication modules which are a generalization of multiplication modules. Let M be an R-module and a multiplicatively closed subset. M is said to be an S-multiplication module if for each submodule N of M there exist and an ideal I of R such that Besides giving many properties of S-multiplication modules, we generalize some results on multiplication modules to S-multiplication modules. Also, we study S-prime submodules in S-multiplication modules. In particular, we generalize prime avoidance lemma for multiplication modules to S -multiplication modules. Furthermore, we characterize multiplication modules in terms of S-multiplication modules. Communicated by Toma Albu
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    On S-multiplication modules (vol 48, pg 3398, 2020)
    (Taylor & Francis Inc, 2021) Anderson, D. D.; Arabaci, Tarik; Tekir, Unsal; Koc, Suat
    In this corrigendum, we give an example showing that the implication (2) double right arrow (1) of Proposition 4 is not true in general. Also, we provide the correct version of Proposition 4.
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    S-Artinian rings and finitely S-cogenerated rings
    (World Scientific Publ Co Pte Ltd, 2020) Sevim, Esra Sengelen; Tekir, Unsal; Koc, Suat
    Let 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.