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Fuzzy Prime And Semiprime S-Subacts Over Monoids

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  • J. AHSAN

    ()
    (Department of Mathematics, Faculty of Applied Sciences, International Islamic University, Islamabad, Pakistan)

  • K. SAIFULLAH

    ()
    (Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia)

  • M. SHABIR

    ()
    (Department of Mathematics, Quid-i-Azam University, Islamabad, Pakistan)

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    Abstract

    In this paper, we introduce the notions of fuzzy prime and fuzzy semiprime S-subacts, where S is a monoid with a zero and S-acts are representations of S. We establish their basic properties and prove some fundamental results in a fuzzy context, analogous to the results in ordinary semigroups and S-acts. It is shown, among other results, that if a fuzzy right S-subact is fuzzy irreducible, then the difference between fuzzy prime and fuzzy semiprime disappears.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 03 (2007)
    Issue (Month): 01 ()
    Pages: 41-55

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    Handle: RePEc:wsi:nmncxx:v:03:y:2007:i:01:p:41-55

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    Related research

    Keywords: Fuzzy S-subacts; fuzzy irreducible ideals; fuzzy irreducible S-subacts; fuzzy annihilator; fuzzy prime and fuzzy semiprime S-subacts;

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