On Mori domains and commutative rings with \(CC^{\perp}\). II
type: Item
instance of: scholarly article
title: On Mori domains and commutative rings with \(CC^{\perp}\). II
zbMATH Open document ID: 0711.13006
DOI: 10.1016/0022-4049(89)90068-6
author: Moshe Roitman
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: This paper is a sequel to part I [ibid. 56, No.3, 247-268 (1989; Zbl 0677.13005)]. A commutative domain A is Mori if and only if it satisfies the ascending chain condition on divisorial ideals (so that e.g. a domain A is Krull if and only if it is Mori and completely integrally closed). The main result here is the construction of a Mori domain A such that AX is not Mori, thus confirming a conjecture by \textit{P. Ribenboim} [``Power series over Mori domains'', Queen's Univ. Prepr. No.21 (1986); see also Commun. Algebra 16, No.5, 1017-1026 (1988; Zbl 0699.13009)]. Some further results and examples concerning finitely generated over- rings and pullbacks of Mori domains are also included.
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13B25
zbMATH DE Number: 4168808
zbMATH Keywords: ACC on annihilators
zbMATH Keywords: power series ring
zbMATH Keywords: Mori domain
reviewed by: Kenneth A. Brown
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90068-6
OpenAlex ID: W4212982265
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description: scientific article; zbMATH DE number 4168808