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IMCS/Publications/QRS/Issues/QRS v.16, n.2 (20), 2008/

Fuzzy ideals in ordered semigroups I

Authors: A. Khan, Y. B. Jun and M. Shabir

Abstract

We prove that: a regular ordered semigroup S is left simple if and only if every fuzzy left ideal of S is a constant function. We also show that an ordered semigroup S is left (resp. right) regular if and only if for every fuzzy left (resp. right) ideal f of S we have, f(a)=f(a2) for every a in S. Further, we characterize some semilattices of ordered semigroups in terms of fuzzy left(resp. right) ideals. In this respect, we prove that an ordered semigroup S is a semilattice of left (resp. right) simple semigroups if and only if for every fuzzy left(resp. right) ideal f of S we have, f(a)=f(a2) and f(ab)=f(ba) for all a,b in S.

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