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    On S-prime submodules
    (Turkish Journal of Mathematics, 2019-01-03) Sevim, Esra Şengelen; Arabacı, Tarık
    ABSTRACT: 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 ? 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) ? S = ? is called an S -prime submodule if there is an s ? S such that am ? P implies sa ? (P :R M) or sm ? P. Also, an R-module M is called S -torsion-free if ann(M) ? S = ? and there exists s ? S such that am = 0 implies sa = 0 or sm = 0 for each a ? R and m ? 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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    Spherically symmetric finsler metrics with constant ricci and flag curvature
    (University of Debrecen, Institute of Mathematics, 2015) Sevim, Esra Şengelen
    Spherically symmetric metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a spherically symmetric metric on Rn. In this paper, we study spherically symmetric metrics with constant Ricci curvature (tensor) and constant flag curvature. © 2015 University of Debrecen Institute of Mathematics. All rights reserved.