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SM ISO690:2012 KHAN, Asghar, JUN, Young-Bae, SHABIR, Muhammad. Fuzzy ideals in ordered semigroups I. In: Quasigroups and Related Systems, 2008, vol. 16, nr. 2(20), pp. 207-220. ISSN 1561-2848. |
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Quasigroups and Related Systems | ||||||
Volumul 16, Numărul 2(20) / 2008 / ISSN 1561-2848 | ||||||
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Pag. 207-220 | ||||||
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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 ∈ 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 ∈ S .
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Cuvinte-cheie Fuzzy subset, fuzzy left(resp. right) ideal, semilattice of left (resp. right) simple semigroups, ordered semigroup |
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