Integral domains with highly nonunique factorization
type: Item
instance of: scholarly article
title: Integral domains with highly nonunique factorization
zbMATH Open document ID: 0896.13014
DOI: 10.1007/BF03322066
author: Dong Je Kwak
author: D. D. Anderson
author: Scott T. Chapman
published in: Results in Mathematics
publication date: 1998-09-27T00:00:00Z
review text: For a positive integer \(n\), an atomic domain \(R\) is defined in the paper to be completely non-\(n\)-factorial if the product of any \(n\) atoms is divisible by the product of any \(n-1\) atoms. The authors prove that a domain \(R\) is completely non-\(n\)-factorial for some \(n\geq 2\) iff \(R\) is an atomic pseudo-valuation domain, equivalently, \((R,M)\) is quasilocal with \([M:M]\) a DVR with maximal ideal \(M\).
Mathematics Subject Classification ID: 13F15
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 1140102
zbMATH Keywords: pseudo-valuation domain
zbMATH Keywords: completely non-factorial domain
zbMATH Keywords: atomic domain
reviewed by: Moshe Roitman
MaRDI profile type: Publication
cites work: Elasticity of factorizations in integral domains
cites work: Factorization in integral domains
cites work: Criteria for unique factorization in integral domains
cites work: Cohen-Kaplansky domains: Integral domains with a finite number of irreducible elements
cites work: Q4343533
cites work: Rings With a Finite Number of Primes. I
cites work: Pseudo-valuation domains
full work available at URL: https://doi.org/10.1007/bf03322066
OpenAlex ID: W2028148995
Recommended article: Q4254114
Recommended article: Q2981100
Recommended article: Q5465406
Recommended article: Almost excellent unique factorization domains
Recommended article: An Integral Domain Lacking Unique Factorization into Irreducibles
Recommended article: Factorization in integral domains
Recommended article: On unique factorization domains
Recommended article: Some Results on Factorization in Integral Domains
Recommended article: Factoring ideals in integral domains
description: scientific article; zbMATH DE number 1140102