Quadratic KU1 of localizations

The quadratic KU1(R,Λ) defined by quadratic group U(R,Λ) is an analog in the theory of K1(R) defined by general linear group GL(R). In this article, we deal with the Cohn localizations of form rings and compute the quadratic KU1(R,Λ) of the associative rings in a class which includes formal power series rings and the augmentation localization of group rings.