Examples of Jaffard domains
type: Item
instance of: scholarly article
title: Examples of Jaffard domains
zbMATH Open document ID: 0656.13011
DOI: 10.1016/0022-4049(88)90027-8
author: Alain Bouvier
author: S. Kabbaj
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let A be a commutative domain of finite Krull dimension. The valuative dimension \(\dim_ vA\) is an integer n for which every overring of A in the quotient field \(K=Frac(A)\) has dimension \(\leq n\) and there exists an overring of A in K of dimension n or, equivalently, for which dim A[X\({}_ 1,...,X_ n]=2n\). This notion was introduced by \textit{P. Jaffard} [``Theorie de la dimension dans les anneaux de polynômes'', Mém. Sci. Math. 146 (1960; Zbl 0096.025)]. It has the property \(\dim_ vA[X_ 1,...,X_ n]=n+\dim_ vA\) which is not satisfied generally by the Krull dimension dim. In general, \(\dim (A)\leq \dim_ vA\) and the difference \(\dim_ vA-\dim (A)\) can be arbitrarily large. So it is quite natural to study rings A with \(\dim (A)=\dim_ vA\). Such a ring is called a Jaffard domain. This paper presents examples of Jaffard domains in order to point out the connection between Jaffard domains, Kaplansky strong S-domains, universally strong S-domains and UFD.
reviewed by: Trung Ngo Viet
Mathematics Subject Classification ID: 13C15
zbMATH DE Number: 4071055
zbMATH Keywords: valuative dimension
zbMATH Keywords: Krull dimension
zbMATH Keywords: Jaffard domain
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90027-8
OpenAlex ID: W2002890668
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description: scientific article; zbMATH DE number 4071055