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1995•Communications in AlgebraRequires access

Integral closure of a filtration relative to a module

Henri Dichi

Open publisher page 3 citations

Abstract

In this paper, the concept of integral dependence over a filtration f on a ring A, relative to a module M is introduced and several properties concerning the integral closure ClosA(f, M) of a pair (f, M) are established. Specially, we give a complete description of ClosA(f, M) when A is a noetherian ring of Krull dimension at most 1. The paper is closed by giving a constructive method to express the integral closure of a pair (f, A) when f is strongly AP an a noetherian integral domain of Krull dimension 1.

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What this paper is about

In this paper, the concept of integral dependence over a filtration f on a ring A, relative to a module M is introduced and several properties concerning the integral closure ClosA(f, M) of a pair (f, M) are established. Specially, we give a complete description of ClosA(f, M) when A is a noetherian ring of Krull dimension at most 1. The paper is closed by giving a constructive method to express the integral closure of a pair (f, A) when f is strongly AP an a noetherian integral domain of Krull dimension 1.

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Available abstract

In this paper, the concept of integral dependence over a filtration f on a ring A, relative to a module M is introduced and several properties concerning the integral closure ClosA(f, M) of a pair (f, M) are established. Specially, we give a complete description of ClosA(f, M) when A is a noetherian ring of Krull dimension at most 1. The paper is closed by giving a constructive method to express the integral closure of a pair (f, A) when f is strongly AP an a noetherian integral domain of Krull dimension 1.

Key concepts: Krull dimension, Mathematics, Closure (psychology), Noetherian, Regular local ring, Integral domain, Filtration (mathematics), Pure mathematics

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