Group Rings and Hopf-Galois Theory in Maple

Abstract

As the title implies, the subject is known as Hopf-Galois theory which attempts to expand the notions of classical Galois theory to more general settings. While the particulars of the subject are not the main focus of this discussion, the principal objects under study, namely group rings and certain subrings of these group rings are of interest. The computational demands involved in describing them and performing computations in them, are what motivated the development, in Maple, of a collection of tools to accomplish this task. Before going further, some background would be appropriate and will help frame the discussion to follow.