Kurosh-Amitsur right Jacobson radicals of type-1 and 2 for right near-rings.
type: Item
instance of: scholarly article
title: Kurosh-Amitsur right Jacobson radicals of type-1 and 2 for right near-rings.
zbMATH Open document ID: 1146.16026
author: Ravi Srinivasa Rao
author: K. Siva Prasad
author: T. Srinivas
published in: Results in Mathematics
publication date: 2008-06-10T00:00:00Z
review text: Earlier the first two authors defined and investigated the right Jacobson radicals \(J_1^r\) and \(J_2^r\) for right near-rings [\textit{R. Srinivasa Rao} and \textit{K. Siva Prasad}, Kyungpook Math. J. 46, No. 4, 603-613 (2006; Zbl 1122.16037)]. Further properties of these two radicals which are of interest from a general radical theoretic view are determined here. In particular, it is shown that \(J_\nu^r\), \(\nu\in\{1,2\}\), is a Kurosh-Amitsur radical in the variety of all near-rings in which the constant part forms an ideal. This means \(J_1^r\) is a Kurosh-Amitsur radical in the variety of zero-symmetric near-rings which is not the case for the left Jacobson radical \(J_1\). However, examples are provided to show that for each \(\nu\in\{1,2\}\), \(J_\nu^r\) is not s-hereditary (and thus not ideal-hereditary) in the variety of zero-symmetric near-rings.
reviewed by: Stefan Veldsman
Mathematics Subject Classification ID: 16Y30
Mathematics Subject Classification ID: 16N80
Mathematics Subject Classification ID: 16N20
zbMATH DE Number: 5285870
zbMATH Keywords: near-rings
zbMATH Keywords: right Jacobson radical
zbMATH Keywords: Kurosh-Amitsur radicals
zbMATH Keywords: varieties of near-rings
MaRDI profile type: Publication
full work available at URL: s00025-007-0280-2
OpenAlex ID: W1998308762
DOI: 10.1007/S00025-007-0280-2
description: scientific article; zbMATH DE number 5285870