On Herstein's conjecture
type: Item
instance of: scholarly article
title: On Herstein's conjecture
zbMATH Open document ID: 0782.16016
author: V. A. Mushrub
published in: Moscow University Mathematics Bulletin
publication date: 1993-03-18T00:00:00Z
review text: Let \(R\) be a left noetherian ring with identity element and \(A\), \(B\) are left ideals of \(R\) such that \(B\subseteq A\) and for any element \(x\in A\) there exists an integer \(n = n(x) \geq 1\) such that \(x^ n \in B\). The author proves that \(A^ m \subseteq B\) for some integer \(m \geq 1\) if either \(B^{k+1} = B^ k\) for some \(k \geq 1\) or \(B + P/P\) is a left artinian \(R/P\)-module (where \(P\) is the lower nil radical of \(R\)).
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 16P40
zbMATH DE Number: 130715
zbMATH Keywords: left noetherian ring
zbMATH Keywords: left ideals
zbMATH Keywords: lower nil radical
reviewed by: Yu. N. Maltsev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 130715