On Nagata's pairwise algorithm
type: Item
instance of: scholarly article
title: On Nagata's pairwise algorithm
zbMATH Open document ID: 0829.13012
author: Wen-Yao Chen
author: Ming-Guang Leu
published in: Journal of Algebra
publication date: 1996-01-17T00:00:00Z
review text: The author studies some properties of a commutative ring with a pairwise algorithm, a concept extending that of Euclidean algorithm introduced by \textit{M. Nagata} [in: Commutative Algebra and Combinatorics, US-Jap. joint Semin., Kyoto 1985, Adv. Stud. Pure Math. 11, 167-171 (1987; Zbl 0701.13008)]. For instance if \(E_1 = E_2 \oplus E_3\) where \(E_i\) are rings, then \(E\) has a pairwise algorithm if and only if \(E_2\) and \(E_3\) have a pairwise algorithm. If an integral domain \(E\) has a pairwise algorithm and \(S\) is a multiplicative subset not containing 0, then the ring of fractions \(S^{-1}E\) has a pairwise algorithm.
Mathematics Subject Classification ID: 13F07
zbMATH DE Number: 589935
zbMATH Keywords: pairwise algorithm
zbMATH Keywords: Euclidean algorithm
reviewed by: N. Sankaran
MaRDI profile type: Publication
full work available at URL: jabr.1994.1106
OpenAlex ID: W2003749300
DOI: 10.1006/JABR.1994.1106
description: scientific article; zbMATH DE number 589935