On p.p.-rings which are reduced.
type: Item
instance of: scholarly article
title: On p.p.-rings which are reduced.
zbMATH Open document ID: 1119.16002
DOI: 10.1155/IJMMS/2006/34694
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2007-06-13T00:00:00Z
full work available at URL: https://eudml.org/doc/53363
review text: A unital ring \(R\) is (left) right p.p. if every (left) right principal ideal of \(R\) is projective. \(R\) is called p.p. if it is left and right p.p. The main theorem of the paper states that a p.p.-ring contains no nonzero nilpotent elements (i.e., it is reduced) if and only if it has no subrings isomorphic to the \(2\times 2\) upper triangular matrices over the ring of integers, \(\mathbb{Z}\), or to the \(2\times 2\) upper triangular matrices over the fields of residues modulo primes, \(\mathbb{Z}_p\).
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 5163991
zbMATH Keywords: pp-rings
zbMATH Keywords: reduced rings
zbMATH Keywords: projective principal right ideals
zbMATH Keywords: nilpotent elements
zbMATH Keywords: rings of upper triangular matrices
zbMATH Keywords: idempotents
author: Xiaojiang Guo
author: K. P. Shum
reviewed by: Simion Sorin Breaz
MaRDI profile type: Publication
cites work: A note on extensions of Baer and P. P. -rings
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cites work: PP-rings of generalized power series
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description: scientific article; zbMATH DE number 5163991