Elasticity of factorizations in atomic monoids and integral domains
type: Item
instance of: scholarly article
title: Elasticity of factorizations in atomic monoids and integral domains
zbMATH Open document ID: 0844.11068
author: Franz Halter-Koch
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1996-09-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/93636
full work available at URL: jtnb7-2.html
review text: The elasticity \(\rho (R)\) of an atomic integral domain \(R\) is defined as the supremum of the ratios \(m/n\) taken over all equalities \(u_1 u_2 \dots u_m= v_1 v_2 \dots v_n\) with irreducible \(u_i\), \(v_j\). This notion is studied using the language of atomic monoids and it is shown that if \(R\) is a Krull domain, then \(\rho (R)\) depends only on the divisor class group of \(R\) and the set of divisor classes containing prime divisors. Also a characterization is given of orders in an algebraic number field which have finite elasticity.
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 858570
zbMATH Keywords: length of factorization
zbMATH Keywords: orders with finite elasticity
zbMATH Keywords: elasticity
zbMATH Keywords: atomic integral domain
zbMATH Keywords: atomic monoids
zbMATH Keywords: Krull domain
zbMATH Keywords: divisor class group
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
Wikidata QID: Q114013330
OpenAlex ID: W2069513340
cites work: Elasticity of factorizations in integral domains
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cites work: Longueurs des décompositions en produits d'éléments irréductibles dans un anneau de Dedekind. (Lengths of decompositions in products of irreducible elements in a Dedekind ring)
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DOI: 10.5802/JTNB.147
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description: scientific article; zbMATH DE number 858570