Non-Cohen-Macaulay unique factorization domains in small dimensions
type: Item
instance of: scholarly article
title: Non-Cohen-Macaulay unique factorization domains in small dimensions
zbMATH Open document ID: 1209.13022
author: Agustin Marcelo
author: Peter Schenzel
published in: Journal of Symbolic Computation
publication date: 2011-03-31T00:00:00Z
review text: In 1964 \textit{M. P. Murthy} [see Arch. Math. 15, 418--420 (1964; Zbl 0123.03401)] showed that a Cohen-Macaulay affine factorial domain is in fact a Gorenstein ring. Later, Samuel asked for the existence of a local unique factorization domain which is not a Cohen-Macaulay ring. The first example of a non-Cohen-Macaulay factorial domain was constructed by \textit{M.-J. Bertin} [see, C. R. Acad. Sci., Paris, Sér. A 264, 653--656 (1967; Zbl 0147.29503)]. In the paper under review the authors construct examples of non-Cohen-Macaulay unique factorization domains in small dimension. They find a unique factorization domain of dimension 3 which is not a Cohen-Macaulay ring. Moreover, there is an example of a five-dimensional affine ring \(S\) over a field \(k\) with the property that \(S\) is a non-Cohen-Macaulay unique factorization domain whenever Char \(k=2\), while it is a Gorenstein non-factorial ring for Char \(k\neq 2\).
reviewed by: Siamak Yassemi
Mathematics Subject Classification ID: 13F15
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 5872536
zbMATH Keywords: factorial ring
zbMATH Keywords: Cohen-Macaulay ring
zbMATH Keywords: factorial closure
describes a project that uses: SINGULAR
describes a project that uses: Macaulay2
MaRDI profile type: Publication
full work available at URL: j.jsc.2010.10.010
OpenAlex ID: W2018406931
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DOI: 10.1016/J.JSC.2010.10.010
description: scientific article; zbMATH DE number 5872536