Classical rings of quotients of semiprime PI-rings
type: Item
instance of: scholarly article
title: Classical rings of quotients of semiprime PI-rings
zbMATH Open document ID: 0799.16018
DOI: 10.1007/BF02260926
published in: Algebra and Logic
publication date: 1994-04-12T00:00:00Z
review text: The author considers the problem, when a semiprime P. I. ring has a classical quotient ring. Examples of Bergman and Markov show that there exist semiprime P. I. rings without classical quotient rings. The main result of the paper under review is that a semiprime P. I. ring \(R\), which is right p. p. and with an upper bound \(n\) of nilpotency index of elements of \(R\) has a classical quotient ring, \(Q_{cl}(R)\). Moreover, \(Q_{cl}(R)\) is strongly right \(n\) regular P. I. and \(n\)-regular p. p., \(P \to P \cap R\) gives a bijection between \(\text{Max Spec }Q_{cl}(R)\) and \(\text{Min Spec}(R)\). A major tool in the proof is a study of the ring \(Q_ e(R)\) generated by \(R\) and the Boolean ring of central idempotents of \(Q(R)\), (the maximal quotient ring of \(R\)).
Mathematics Subject Classification ID: 16R20
Mathematics Subject Classification ID: 16U20
zbMATH DE Number: 536684
zbMATH Keywords: semiprime P. I. ring
zbMATH Keywords: classical quotient ring
zbMATH Keywords: central idempotents
author: K. I. Beidar
reviewed by: Søren Jøndrup
MaRDI profile type: Publication
cites work: Q4187932
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full work available at URL: https://doi.org/10.1007/bf02260926
OpenAlex ID: W2012572086
description: scientific article; zbMATH DE number 536684