Hopf Orders and a Generalization of a Theorem of L. R. McCulloh Original Research Article

Let K be an algebraic number field with ring of integers image and let G be an elementary abelian group of order lk. Let image be a Hopf order in KG and let image be its dual. An order image in a Galois G-extension of K is a semilocal principal homogeneous space over image if imagel is a principal homogeneous space over imagel and image is integrally closed away from l. We define a map ψ from the group of such image to the locally free classgroup Cl(image). Assuming that image admits C congruent with imagelk×subset of or equal to Aut(G), we describe the image of ψ in terms of a Stickelberger ideal in imageC. This generalizes a result of L. R. McCulloh on the classes in Cl(imageG) realized by tame rings of integers.