Lifting chains of prime ideals to paravaluation rings
type: Item
instance of: scholarly article
title: Lifting chains of prime ideals to paravaluation rings
zbMATH Open document ID: 0962.13020
DOI: 10.1007/BF02904237
author: David E. Dobbs
publication date: 2001-06-14T00:00:00Z
review text: Let \(R\subset T\) be a unital extension of commutative rings and let \(\{P_\alpha \mid\alpha \in I\}\) be a chain of prime ideals of \(R\). It is proved that \(R\) is contained in some paravaluation ring \(V\) of \(T\) such that \(V\) has a chain of prime ideals \(Q_\alpha\) satisfying \(Q_\alpha\cap R=P_\alpha\) for each \(\alpha\in I\). It can be further arranged that \(N\cap R=\bigcup P_\alpha\) where \(N\) is such that \((V,N)\) is a paravaluation pair of \(T\). This generalizes a similar result by \textit{Byung Gyun Kang} and \textit{Dong Yeol Oh} [proved in Proc. Am. Math. Soc. 126, No. 3, 645-646 (1998; Zbl 0887.13004)] when \(T\) is a field. The paper contains a sufficient condition for deleting the prefix `para' from the above result and also contains some interesting open problems.
reviewed by: Sudesh Kaur Khanduja
Mathematics Subject Classification ID: 13F30
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13B24
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13A18
zbMATH DE Number: 1462348
zbMATH Keywords: paravaluation ring
zbMATH Keywords: unital extension
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02904237
OpenAlex ID: W2086267641
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1462348