Abstract
The notion of fuzzy multiplication semigroup is introduced using fuzzy ideal. In a fuzzy multiplication semigroup with identity, (i) every fuzzy ideal with sup property whose radical is prime is primary and (ii) every primary fuzzy ideal with sup property is some power of its fuzzy radical. Conditions (i) and (ii) are also found to be sufficient for a commutative semigroup with identity and satisfying some other conditions to be a fuzzy multiplication semigroup.
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