2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65051We 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,α) where P is a finitely generated projective A-module and α:P \to P is an endomorphism. This invariant determines (P,α) 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.21 pages, LaTeX, with minor revisionsK-Theory and HomologyRings and Algebras18F25; 16S10; 16S34; 37C27text