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Prestabilization for $K\sb 1$ of Banach algebras. (English) Zbl 0629.20021
Let A be a ring and B an ideal of A satisfying the n stable range condition. It follows from earlier results of Bass and the first author that the natural map $GL\sb n(B)\to K\sb 1(A,B)$ is onto. The purpose of this paper is to obtain some explicit descriptions of its kernel in various interesting cases including, for example, Banach algebras and others which extend to $K\sb 1(A,B)$ some previous results on $K\sb 1(A)$ due to P. Menal - J. Moncasi and M. Godefroid.
Reviewer: P.Menal

MSC:
 20G35 Linear algebraic groups over adèles and other rings and schemes 20H25 Other matrix groups over rings 18F25 Algebraic $K$-theory and $L$-theory
Full Text:
References:
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