On polynomial extensions of Mori domains over countable fields
type: Item
instance of: scholarly article
title: On polynomial extensions of Mori domains over countable fields
zbMATH Open document ID: 0729.13016
DOI: 10.1016/0022-4049(90)90065-P
author: Moshe Roitman
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: Building on his work in J. Pure Appl. Algebra 61, No.1, 53-77 (1989; Zbl 0711.13006), the author shows that, for a field K, if K is countable then it is contained in a Mori domain A for which A[X] is not Mori. [The converse follows from a paper by \textit{V. Camillo} and \textit{R. Guralnick}; cf. Proc. Am. Math. Soc. 98, 567-568 (1986; Zbl 0608.16020).] This develops a similar result, with the Mori condition replaced by the ACC on annihilators, which was also shown by \textit{J. W. Kerr} [J. Algebra 134, No.2, 344-352 (1990; Zbl 0719.16015)].
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 4204516
zbMATH Keywords: Mori domain
zbMATH Keywords: ACC on annihilators
reviewed by: C. P. L. Rhodes
MaRDI profile type: Publication
cites work: Polynomial Rings Over Goldie Rings are Often Goldie
cites work: The polynomial ring over a Goldie ring need not be a Goldie ring
cites work: Idéaux divisoriels d'un anneau de polynômes
cites work: On Mori domains and commutative rings with \(CC^{\perp}\). I
cites work: On Mori domains and commutative rings with \(CC^{\perp}\). II
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description: scientific article; zbMATH DE number 4204516