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ArticleOriginal scientific text

Title

Some remarks on the altitude inequality

Authors 1

Affiliations

  1. Laboratoire d'algèbre E03/C15, Department of Mathematics, Faculty of Sciences, University of Sfax, Sfax, 3038 Tunisia

Abstract

We introduce and study a new class of ring extensions based on a new formula involving the heights of their primes. We compare them with the classical altitude inequality and altitude formula, and we give another characterization of locally Jaffard domains, and domains satisfying absolutely the altitude inequality (resp., the altitude formula). Then we study the extensions R ⊆ S where R satisfies the corresponding condition with respect to S (Definition 3.1). This leads to a new characterization of integral extensions.

Keywords

ENG
valuation domain, altitude inequality, restrictive altitude inequality, locally Jaffard domain

Bibliography

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Colloquium Mathematicum
1999/80/1
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Pages:
39-52
Main language of publication
English
Received
1998-06-16
Published
1999
Exact and natural sciences