Whitehead Groups of Localizations and the Endomorphism Class Group

Details Whitehead Groups of Localizations and the Endomorphism Class Group Whitehead Groups of Localizations and the Endomorphism Class Group

2002-09-23

arxiv.org/abs/math/0209311v2

Journal of Algebra, Vol 270 (2003) Issue 1, 261-280

Mathematics

K-Theory and Homology

21 pages, LaTeX, with minor revisions

Scientific paper

We compute the Whitehead groups of the associative rings in a class which includes (twisted) formal power series rings and the augmentation localizations of group rings and polynomial rings. For any associative ring A, we obtain an invariant of a pair (P,\alpha) where P is a finitely generated projective A-module and \alpha:P \to P is an endomorphism. This invariant determines (P,\alpha) up to extensions, yielding a computation of the (reduced) endomorphism class group of A. We also refine the analysis by Pajitnov and Ranicki of the Whitehead group of the Novikov ring.

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