FUZZY PRIME AND SEMIPRIMES-SUBACTS OVER MONOIDS

J. Ahsan (), K. Saifullah () and M. Shabir ()
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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

New Mathematics and Natural Computation (NMNC), 2007, vol. 03, issue 01, 41-55

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

Keywords: FuzzyS-subacts; fuzzy irreducible ideals; fuzzy irreducibleS-subacts; fuzzy annihilator; fuzzy prime and fuzzy semiprimeS-subacts (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S1793005707000616

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