ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16 Sonin, Constantin, Department of Algebra, Faculty for Mechanics and Mathematics, Moscow State University, Moscow, Russia 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-Neumann 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. Reference: C. Sonin, Krull Dimension of Malcev-Neumann Rings, Communications in Algebra, to appear in 1998.