Tame Realisable Classes over Hopf Orders

Abstract

LetObe the ring of algebraic integers in a number fieldKand letGbe a finite abelian group. McCulloh has characterised the classes in the locally free classgroup Cl(OG) which are realisable by rings of integers of tame normal extensions ofKwith Galois groupG. We extend this to certain extensions which in general need be neither tame nor normal by replacingOGwith a Hopf order A and introducing the strongly A-tame orders as an analogue of tame rings of integers. We also describe the classes realised by principal homogeneous spaces over the dual of A. © 1998 Academic Press.