Abstract
In the case when R is a Dedekind domain of positive prime characteristic p > 0, we give a parameterisation of the isomorphism classes of the injective indecomposable R ∞-modules. Here R ∞ is the smallest ring extension of R on which the Frobenius morphism acts bijectively. Further, in this case, every injective R ∞-module is the injective hull of a direct sum of injective indecomposable R ∞-modules.
Acknowledgments
I would like to express my thanks to Prof. R. Y. Sharp, who suggested this topic and corrected many of the mistakes in the initial drafts. This work is supported by a fees-only studentship provided by the Engineering and Physical Sciences Research Council of the United Kingdom.