  We characterize the fuzzy left (resp. right) ideals, the fuzzy ideals and the
fuzzy prime (resp. semiprime) ideals of an ordered $\Gamma$-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
$M\times M$, and the cartesian product of two fuzzy prime (resp. semiprime)
ideals of $M$ is a fuzzy prime (resp. semiprime) ideal of $M\times M$. As a
result, if $\mu$ and $\sigma$ are fuzzy left (resp. right) ideals, ideals,
fuzzy prime or fuzzy semiprime ideals of $M$, then the nonempty level subsets
$(\mu\times\sigma)_t$ are so.
