A note on Swan modules. (English) Zbl 0687.16004

The author studies Swan modules over certain non-maximal orders in this note. Motivation for studying such modules was given by Martin Taylor’s work on Galois module structures. Taylor showed that a certain generalized Swan module is an obstruction to the freeness of a ring of integers over its associated order. The author shows for example that the resolvent element lies in the associated order.
Reviewer: R.A.Mollin


16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
11R52 Quaternion and other division algebras: arithmetic, zeta functions
16Gxx Representation theory of associative rings and algebras
16W20 Automorphisms and endomorphisms