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    LOCALLY S-PRIME IDEALS
    (Publ House Bulgarian Acad Sci, 2020) Arabaci, Tarik; Sevim, Esra Sengelen
    Let R be a commutative ring and S be a multiplicatively closed subset of R. Lambda proper ideal P of R is called locally S-prime if P-S is a prime ideal of R-S. It is shown that, P is a locally S-prime ideal if and only if whenever P boolean AND S = ? and if ab is an element of P for some a, b is an element of R, then there exists s is an element of S such that sa is an element of P or sb is an element of P. As a consequence of this fact and well-known properties of prime ideals we obtain some properties of these ideals. Also, all multiplicatively closed subsets S of R that an ideal can be locally S-prime are characterised. Finally, these ideals are studied in an S-Noetherian ring.
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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.