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Atagün, Akın Osman; Sezgin, Aslıhan

Soft substructures of rings, fields and modules. (English) Zbl 1217.16041

Comput. Math. Appl. 61, No. 3, 592-601 (2011).
Summary: 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.

Cited in 30 Documents

MSC:

16Y99 Generalizations
03E72 Theory of fuzzy sets, etc.

Keywords:

soft sets; soft subrings; soft ideals; soft subfields; soft submodules
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\textit{A. O. Atagün} and \textit{A. Sezgin}, Comput. Math. Appl. 61, No. 3, 592--601 (2011; Zbl 1217.16041)
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References:

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