Projective modules of group rings over quadratic number fields

Abstract

Let K be a quadratic number field, Ok its ring of integers, and G a cyclic group of order prime p. In this thesis, we study the kernel group D(O(_K)G) and obtain a number of results concerning its order and structure. For K imaginary, we also investigate the subset R(O(_k)G) of the locally free class group CI(O(_k)G) consisting of classes which occur as rings of integers of tame extensions of K with Galois group isomorphic to G. We calculate R(O(_k)G) under a variety of conditions and obtain, for an arbitrary tame extension L o( K with group G, invariants which determine the class of O(_L) in R(O(_k)G).