ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 19-XX Inassaridze, Hvedri, A. Razmadze Math. Inst., Tbilisi, Georgia Karoubi’s Conjecture for polynomial extensions of stable C*- algebras In the category of normed R-algebras the notion of K*-stability is introduced, playing the same role as K*-regularity for discrete rings. It is proved that algebraic and topological K-groups are isomorphic for K*-stable normed R-algebras. Consequently Karoubi’s Conjecture about the equality of algebraic and toplogical K-theories on the category of stable C*-algebras, confirmed by Suslin and Wodzicki, is extended affirmatively for polynomial extensions of stable C*-algebras. K*-regularity and the fundamental theorem for stable C*-algebras are also obtained.