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Whitehead Groups of Localizations and the Endomorphism Class Group | | Desmond Sheiham
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23 Sep 2002 | | Journal: | Journal of Algebra, Vol 270 (2003) Issue 1, 261-280 | | Subject: | K-Theory and Homology; Rings and Algebras MSC-class: 18F25; 16S10; 16S34; 37C27 | math.KT math.RA | | Abstract: | 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 o 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. | | Source: | arXiv, math.KT/0209311 | | Services: | Forum | Review | PDF | Favorites | |
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