Graded \(P\)-radical
type: Item
instance of: scholarly article
zbMATH Open document ID: 0994.16027
author: Yanli Ren
author: Yao Wang
publication date: 2002-09-17T00:00:00Z
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16N80
zbMATH DE Number: 1623623
zbMATH Keywords: graded rings
zbMATH Keywords: graded radical classes
zbMATH Keywords: prime rings
zbMATH Keywords: graded special radicals
MaRDI profile type: Publication
title: Graded \(P\)-radical
published in: Chinese Quarterly Journal of Mathematics
review text: Let \(M\) be a monoid. An \(M\)-graded ring \(R=\bigoplus(R_m:m\in M)\) is said to be a graded \(M\)-ring, if for each \(a\in R\) there exists a polynomial \(f(x)\) over the integers with zero constant term such that \(f(a)=0\). The class of all \(M\)-graded rings \(P_G\) is a graded radical class in the sense of Kurosh and Amitsur. The class of \(P_G\)-semisimple \(M\)-graded prime rings is a graded special class, whence \(P_G\) is a graded special radical. For \(M\)-graded \(R\)-modules \(V\), \(P_G\)-modules are defined, and it is proved that \(P_G=\bigcap(0:V)\), where \(V\) ranges over all \(R\)-\(P_G\)-modules.
reviewed by: R. Wiegandt
description: scientific article; zbMATH DE number 1623623