Characterizations Of Monoids By The Properties Of Their Intuitionistic Fuzzy Subacts
AbstractIn this paper, we initiate the study of intuitionistic fuzzy subacts of an S-act, where S is a monoid with zero and S-acts are representations of S. We introduce the notions of pure intuitionistic fuzzy, purely intuitionistic maximal and purely intuitionistic fuzzy prime ideals of a monoid. It is shown that the set of purely intuitionistic fuzzy prime ideals of S admits the structure of a topological space, called the pure intuitionistic fuzzy spectrum of S. We also define a pure intuitionistic fuzzy subact of an S-act and call an S-act intuitionistic fuzzy normal if each of its intuitionistic fuzzy subact is pure. Monoids, of which all S-acts are intuitionistic fuzzy normal, are characterized. It is shown among other results that such monoids are right weakly regular.
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Bibliographic InfoArticle provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.
Volume (Year): 06 (2010)
Issue (Month): 01 ()
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Web page: http://www.worldscinet.com/nmnc/nmnc.shtml
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