Soft substructures of rings, fields and modules

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Abstract

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we introduce and study soft subrings and soft ideals of a ring by using Molodtsov's definition of the soft sets. Moreover, we introduce soft subfields of a field and soft submodule of a left R-module. Some related properties about soft substructures of rings, fields and modules are investigated and illustrated by many examples. © 2010 Elsevier Ltd. All rights reserved.

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Atagün, A. O., & Sezgin, A. (2011). Soft substructures of rings, fields and modules. Computers and Mathematics with Applications, 61(3), 592–601. https://doi.org/10.1016/j.camwa.2010.12.005

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