English

Whitehead Groups of Localizations and the Endomorphism Class Group

K-Theory and Homology 2007-05-23 v2 Rings and Algebras

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 \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.

Keywords

Cite

@article{arxiv.math/0209311,
  title  = {Whitehead Groups of Localizations and the Endomorphism Class Group},
  author = {Desmond Sheiham},
  journal= {arXiv preprint arXiv:math/0209311},
  year   = {2007}
}

Comments

21 pages, LaTeX, with minor revisions

R2 v1 2026-07-22T16:47:52.485Z