Dyadic ideal, class group, and tame kernel in quadratic fields

Abstract

For quadratic number fields F with 2∈N F/ Q (F ∗) , we set up the relations between the class of dyadic ideal in narrow class group and the element of order 4 in the tame kernel, and determine the 2 n ( n>2)-rank of the tame kernel of some quadratic number fields and their Tate kernels.