Elasticities of Krull domains with finite divisor class group
type: Item
instance of: scholarly article
title: Elasticities of Krull domains with finite divisor class group
zbMATH Open document ID: 1079.13002
author: K. Kattchee
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: For an atomic domain \(R\), the elasticity \(\rho(R)\) of \(R\) is defined by \[ \rho(R)=\sup\{m/n\mid a_1\cdots a_m=b_1\cdots b_n \text{ for some irreducibles }a_i,b_j\in R\}. \] Let \(G\) be a finite abelian group. Then \({\mathcal Y}(G)\) denotes the set of all values \(\rho(R)\), where \(R\) ranges among all Krull domains with divisor class group \(G\). In this paper, the author studies \({\mathcal Y}(G)\) for some special finite abelian groups \(G\) of the form \({\mathbb Z}_p,\;\mathbb Z_{2p}\), where \(p\) is a prime integer. He also shows that \({\mathcal Y}(\bigoplus_{i=1}^k\mathbb Z_2)=\{1,3/2,4/2,\ldots,(k+1)/2\}\), for any positive integer \(k\).
reviewed by: Martine Picavet-L'Hermitte
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 13C20
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 2083499
zbMATH Keywords: Krull domain
zbMATH Keywords: block monoid
zbMATH Keywords: Diophantine monoid
zbMATH Keywords: elasticity of factorization
zbMATH Keywords: finite abelian group
zbMATH Keywords: divisor class group
MaRDI profile type: Publication
full work available at URL: j.laa.2004.01.007
OpenAlex ID: W2094484792
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DOI: 10.1016/J.LAA.2004.01.007
description: scientific article; zbMATH DE number 2083499