An application of fuzzy ideals techniques to the level subsets of ordered Γ-groupoids

Аннотация

We characterize the fuzzy left (resp. right) ideals, the fuzzy ideals and the fuzzy prime (resp. semiprime) ideals of an ordered Γ-groupoid M in terms of level subsets and we prove that the cartesian product of two fuzzy left (resp. right) ideals of M is a fuzzy left (resp. right) ideal of M × M, and the cartesian product of two fuzzy prime (resp. semiprime) ideals of M is a fuzzy prime (resp. semiprime) ideal of M × M. As a result, if μ and σ are fuzzy left (resp. right) ideals, ideals, fuzzy prime or fuzzy semiprime ideals of M, then the nonempty level subsets (μ × σ)_t are so.