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Abstract : |
In this paper we initiate the study of fuzzy subsystems of an S-system, where S is a monoid with zero and S-systems are representations of S. We introduce the notions of pure fuzzy, purely fuzzy maximal and purely fuzzy prime ideals of a monoid S. It is shown that the set of purely fuzzy prime ideals of S admits the structure of a topological space, called the pure fuzzy spectrum of S. We also define a pure fuzzy subsystem of an S-system and call an S-system fuzzy normal if each of its subsystems is pure fuzzy. Monoids of which all S-systems are fuzzy normal are characterized. It is shown, among other results, that such monoids are right weakly regular., |
