Our main results show that Munn semirings over idempotent semifields possess
more convenient properties than the Munn rings over fields. First, we describe all
centroid sets that can be generated as ideals of the largest weight in Munn semirings
over idempotent semifields. Second, we handle the more general case of all onesided
ideals too. The multiplication in the Munn semirings is not commutative and
the family of arbitrary one-sided ideals is larger than that of two-sided ideals. It is essential to consider all ideals not only in order
to develop theoretical foundations, but also since the larger set of ideals may lead
to design of classification and clustering systems with better properties. Our main
theorem describes all ideals and one-sided ideals with the largest weight in Munn
semirings over idempotent semifields.