Frobenius maps on injective hulls and their applications to tight closure

Abstract

This paper studies Frobenius maps on injective hulls of residue fields of complete local rings with a view towards providing constructive descriptions of objects originating from the theory of tight closure. Specifically, the paper describes algorithms for computing parameter test ideals, and tight closure of certain submodules of the injective hull of residue fields of a class of well-behaved rings that includes all quasi-Gorenstein complete local rings.