Universally catenarian and going-down pairs of rings

Ahmed Ayache; Mabrouk Ben Nasr; Othman Echi; Noômen Jarboui

doi:10.1007/s002090100272

Universally catenarian and going-down pairs of rings

Ahmed Ayache^*
, Mabrouk Ben Nasr
, Othman Echi
, Noômen Jarboui

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

For a ring extension R ⊆ S, (R, S) is called a universally catenarian pair if every domain T, R ⊆ T ⊆ S, is universally catenarian. When R is a field it is shown that the only universally catenarian pairs are those satisfying tr.deg[S : R] ≤ 1. For dimR ≥ 1 several satisfactory results are given. The second purpose of this paper is to study going-down pairs (Definition 5.1). We characterize these pairs of rings and we establish a relationship between universally catenarian, going-down and residually algebraic pairs.

Original language	English
Pages (from-to)	695-731
Number of pages	37
Journal	Mathematische Zeitschrift
Volume	238
Issue number	4
DOIs	https://doi.org/10.1007/s002090100272
State	Published - Dec 2001
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/s002090100272

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abstract = "For a ring extension R ⊆ S, (R, S) is called a universally catenarian pair if every domain T, R ⊆ T ⊆ S, is universally catenarian. When R is a field it is shown that the only universally catenarian pairs are those satisfying tr.deg[S : R] ≤ 1. For dimR ≥ 1 several satisfactory results are given. The second purpose of this paper is to study going-down pairs (Definition 5.1). We characterize these pairs of rings and we establish a relationship between universally catenarian, going-down and residually algebraic pairs.",

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AU - Ayache, Ahmed

AU - Nasr, Mabrouk Ben

AU - Echi, Othman

AU - Jarboui, Noômen

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Y1 - 2001/12

N2 - For a ring extension R ⊆ S, (R, S) is called a universally catenarian pair if every domain T, R ⊆ T ⊆ S, is universally catenarian. When R is a field it is shown that the only universally catenarian pairs are those satisfying tr.deg[S : R] ≤ 1. For dimR ≥ 1 several satisfactory results are given. The second purpose of this paper is to study going-down pairs (Definition 5.1). We characterize these pairs of rings and we establish a relationship between universally catenarian, going-down and residually algebraic pairs.

AB - For a ring extension R ⊆ S, (R, S) is called a universally catenarian pair if every domain T, R ⊆ T ⊆ S, is universally catenarian. When R is a field it is shown that the only universally catenarian pairs are those satisfying tr.deg[S : R] ≤ 1. For dimR ≥ 1 several satisfactory results are given. The second purpose of this paper is to study going-down pairs (Definition 5.1). We characterize these pairs of rings and we establish a relationship between universally catenarian, going-down and residually algebraic pairs.

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Universally catenarian and going-down pairs of rings

Abstract

ASJC Scopus subject areas

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