Krull dimension of Malcev-Neumann rings

It is known that if R is a right noetherian ring, then the corresponding Malcev-Neumann ring R * ((G)) is right noetherian and r.K.dim(R) = r.K.dim(R * ((G))). We prove that the right noetherianness is a necessary condition for a Malcev-Neuman ring to have right Krull dimension. Also, we consider uniform dimension of Malcev-Neumann rings. The results obtained are applied to some other ring constructions.