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Soft substructures of rings, fields and modules. (English) Zbl 1217.16041
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:
 16Y99 Generalizations of associative rings and algebras 03E72 Fuzzy set theory