Frobenius Maps on Injective Hulls and Their Applications to Tight Closure
نویسنده
چکیده
This paper studies Frobenius maps on injective hulls of residue fields of complete local rings with a view toward 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 which includes all quasiGorenstein complete local rings.
منابع مشابه
Parameter Test Ideals of Cohen Macaulay Rings
The main aim of this paper is to provide a description of parameter test ideals of local Cohen-Macaulay rings of prime characteristic p. The nature of this description will be such that it will allow us to give an algorithm for producing these ideals. The results in this paper will follow from an analysis of Frobenous maps on injective hulls of the residue fields of the rings under consideratio...
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For a one-dimensional local domain CM constructed by Akizuki, we find residue maps which give rise to a local duality. The completion of CM is described using these residue maps. Injective hulls of a given module are all isomorphic. For this reason, people often speak of the injective hull to indicate its “uniqueness”. However, isomorphisms between these injective hulls are not canonical. In fa...
متن کاملar X iv : m at h / 02 09 36 5 v 2 [ m at h . A C ] 2 7 Se p 20 02 RESIDUES FOR AKIZUKI ’ S ONE - DIMENSIONAL LOCAL DOMAIN
For a one-dimensional local domain CM constructed by Akizuki, we find residue maps which give rise to a local duality. The completion of CM is described using these residue maps. Injective hulls of a given module are all isomorphic. For this reason, people often speak of the injective hull to indicate its “uniqueness”. However, isomorphisms between these injective hulls are not canonical. In fa...
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