ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: Albu, Toma, University of Wisconsin–Milwaukee, USA Global Krull dimension and global dual Krull dimension of rings Associated with any ring R are two ordinal numbers α and β. The ordinal α (respectively, β) is the supremum of the (dual) Krull dimensions of all the right R-modules which have (dual) Krull dimension. In this talk we investigate these ordinals and relationships between them for the following classes of rings: arbitrary noncommutative rings, commutative rings, valuation domains, valuation rings, and rings whose completion have a Morita duality. We denote α by r. gl. k(R), β by r. gl. k^{0}(R) and refer to them as the right global Krull dimension and right global dual Krull dimension of R, respectively. The results which will be presented have been obtained jointly with Patrick F. Smith (University of Glasgow, UK) or with Peter Vámos (University of Exeter, UK).