Abstract
We introduce the notion of the Weyl group of a number ring. After that, we give a matrix approach to the study of the ideal class group of a number field, the Bass exact sequence of K-theory of the extension functor, and the capitulation kernel of an extension of number fields.
ACKNOWLEDGMENTS
I would like to thank A. J. Berrick, CheeWhye Chin, M. Karoubi, and T. Lambre for many helpful discussions and suggestions. I also want to thank the referee for careful reading of the manuscript with a lot of helpful comments and suggestions.
I am grateful to Xiang Sun who helped me solve problems in TEX-typing.