Right unique factorization domains
type: Item
instance of: scholarly article
title: Right unique factorization domains
zbMATH Open document ID: 0815.16015
author: Raymond A. Beauregard
published in: Rocky Mountain Journal of Mathematics
publication date: 1994-09-28T00:00:00Z
review text: The author's aim is to study a notion of one-sided unique factorization domain (UFD) which is stronger than the similarity-UFD defined by \textit{P. M. Cohn} [Am. Math. Mon. 80, 1-18 (1973; Zbl 0256.13011)] but reduces to the usual form in the commutative case. A right-UFD is defined as an atomic integral domain such that for any two complete factorizations of an element, \(c = a_ 1 \dots a_ m = b_ 1 \dots b_ n\), where \(a_ i\), \(b_ j\) are atoms, one has \(m = n\) and for some permutation \(\pi\) of \(1,\dots,n\), \(a_ i\) is right associated to \(b_{\pi(i)}\). For a right invariant ring, being a right-UFD is shown to be equivalent to being a similarity-UFD, but an example shows that such a ring need not be a left- UFD (defined correspondingly); however, this does follow if the ring is also left Ore.
Mathematics Subject Classification ID: 16U30
Mathematics Subject Classification ID: 16U10
Mathematics Subject Classification ID: 16U20
Mathematics Subject Classification ID: 13F15
zbMATH DE Number: 645214
zbMATH Keywords: Ore domain
zbMATH Keywords: one-sided unique factorization domain
zbMATH Keywords: right-UFD
zbMATH Keywords: atomic integral domain
zbMATH Keywords: complete factorizations
zbMATH Keywords: right invariant ring
zbMATH Keywords: similarity-UFD
reviewed by: Paul M. Cohn
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072412
OpenAlex ID: W2043100116
cites work: Unique Factorization Domains
cites work: Q5534940
DOI: 10.1216/RMJM/1181072412
description: scientific article; zbMATH DE number 645214