Weyl Groups, Ideal Class Groups and the K-Theory of the Extension Functor

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.

Key Words:

• Capitulation kernel
• K-theory of functor
• Matrix
• Number theory

2010 Mathematics Subject Classification:

• 11R29
• 19D55

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 T_EX-typing.