On the Krull and valuative dimension of \(D+XD_ S[X]\) domains
type: Item
instance of: scholarly article
title: On the Krull and valuative dimension of \(D+XD_ S[X]\) domains
zbMATH Open document ID: 0698.13003
DOI: 10.1016/0022-4049(90)90069-T
author: Marco Fontana
author: S. Kabbaj
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: This paper is concerned with the integral domain \(D^{(S,r)}=D+(X_ 1,X_ 2,...,X_ r)D_ S[X_ 1,...,X_ r]\), where D is an integral domain and S is a multiplicative subset of D. \textit{Costa}, \textit{Mott} and \textit{Zafrullah} considered the prime ideal structure of such domains where \(r=1\). The authors extend that work to \(n>1\). In particular they determine when \(D^{(S,r)}\) is a strong S-domain, a stably strong S- domain, a catenarian domain and a universally catenarian domain. As a consequence, they obtain a new class of non-Noetherian universally catenarian domains. Further, they provide an explicit formula for the Krull dimension of \(D^{(S,r)}\).
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 4144102
zbMATH Keywords: (D\(+I)\)-rings
zbMATH Keywords: stably strong S-domain
zbMATH Keywords: universally catenarian domain
zbMATH Keywords: Krull dimension
reviewed by: Ann K. Boyle
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4144102