Heredity of radicals in a class of noncommutative Jordan rings
type: Item
instance of: scholarly article
title: Heredity of radicals in a class of noncommutative Jordan rings
zbMATH Open document ID: 0835.17001
DOI: 10.1007/BF01209089
author: V. P. Chuvakov
published in: Mathematical Notes
publication date: 1995-09-12T00:00:00Z
review text: A ring is called noncommutative Jordan if it satisfies the identities \((x, y, x)= (x^2, y, x)= 0\). Let \(R\) be an associative commutative ring containing \(1/6\) and \({\mathcal M}\) the class of noncommutative Jordan rings over \(R\) satisfying the identity \(([x, y], z,z) =0\). The author proves that if \(r\) is a radical in \({\mathcal M}\) then an ideal of an \(r\)- semisimple ring is \(r\)-semisimple. This implies that the locally nilpotent radical in \({\mathcal M}\) is hereditary. (The existence of the locally nilpotent radical in \({\mathcal M}\) has been proved by \textit{I. P. Shestakov} [Algebra Logic 10, 252-280 (1973); translation from Algebra Logika 10, 407-448 (1971; Zbl 0259.17001)]).
Mathematics Subject Classification ID: 17A15
Mathematics Subject Classification ID: 17A65
zbMATH DE Number: 795656
zbMATH Keywords: hereditary radicals
zbMATH Keywords: noncommutative Jordan rings
zbMATH Keywords: locally nilpotent radical
reviewed by: Boris Vernikov
MaRDI profile type: Publication
cites work: On local finiteness in the sense of Shirshov
cites work: Heredity of radicals of rings of type \((\gamma,\delta)\)
cites work: Q3772389
full work available at URL: https://doi.org/10.1007/bf01209089
OpenAlex ID: W2060136374
description: scientific article; zbMATH DE number 795656