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Zbl 1217.16041
Atagün, Ak in Osman; Sezgin, Asl ihan
Soft substructures of rings, fields and modules. (English)
[J] Comput. Math. Appl. 61, No. 3, 592-601 (2011). ISSN 0898-1221

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.

MSC 2000:: *16Y99 Generalizations of associative rings and algebras
03E72 Fuzzy sets (logic)

Keywords: soft sets; soft subrings; soft ideals; soft subfields; soft submodules

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