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Fuzzy ideals in ordered semigroups I
Authors: A. Khan, Y. B. Jun and M. Shabir
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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.Fulltext
– 0.24 Mb
Contents
- Redefined fuzzy Lie subalgebras
- Generalized fuzzy subquasigroups
- Secondary representation of semimodules over a commutative semiring
- Groups homeomorphisms: topological characteristics, invariant measures and classification
- Fuzzy regular congruence relations on hyper BCK-algebras
- On prolongations of quasigroups
- On fuzzy relations and fuzzy quotient Gamma-groups
- Fuzzy ideals in ordered semigroups I
- The action of G22 on PL(Fp)
- Simple hyper K-algebras
- Prime bi-ideals in ternary semigroups
