On weak \(\pi\)-regularity of rings whose prime ideals are maximal
type: Item
instance of: scholarly article
title: On weak \(\pi\)-regularity of rings whose prime ideals are maximal
zbMATH Open document ID: 0942.16012
DOI: 10.1016/S0022-4049(98)00177-7
author: Chan Yong Hong
author: Nam Kyun Kim
author: Tai Keun Kwak
author: Yang Lee
published in: Journal of Pure and Applied Algebra
publication date: 2000-08-01T00:00:00Z
review text: A ring \(R\) is 2-primal if the prime radical is the set of all nilpotent elements of \(R\). \(R\) is weakly \(\pi\)-regular if for each \(x\in R\), there exists a natural number \(n\), depending on \(x\), such that \(x^n\in(x^nRx^nR)\cap(Rx^nRx^n)\). The authors investigate the connections between the weak \(\pi\)-regularity and the maximality of prime ideals in 2-primal rings, right quasi-duo rings and PI-rings, respectively, (\(R\) is right quasi-duo if every maximal right ideal of \(R\) is two-sided).
reviewed by: Xue Weimin
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16U80
zbMATH DE Number: 1398846
zbMATH Keywords: prime radical
zbMATH Keywords: nilpotent elements
zbMATH Keywords: weak \(\pi\)-regularity
zbMATH Keywords: maximality of prime ideals
zbMATH Keywords: 2-primal rings
zbMATH Keywords: right quasi-duo rings
zbMATH Keywords: PI-rings
zbMATH Keywords: maximal right ideals
MaRDI profile type: Publication
full work available at URL: s0022-4049(98)00177-7
OpenAlex ID: W2043311341
Recommended article: ON WEAK II-REGULARITY AND THE SIMPLICITY OF PRIME FACTOR RINGS
Recommended article: On weaklyS-prime ideals of commutative rings
Recommended article: On \(S\)-weakly prime ideals of commutative rings
Recommended article: Q4594435
Recommended article: Q4245029
Recommended article: A Connection Between Weak Regularity and the Simplicity of Prime Factor Rings
Recommended article: On weakly semiprime ideals of commutative rings
Recommended article: Q4380208
Recommended article: ON RINGS IN WHICH EVERY IDEAL IS WEAKLY PRIME
Recommended article: Q4484979
description: scientific article; zbMATH DE number 1398846