Alternator ideal in weakly alternative rings
type: Item
instance of: scholarly article
title: Alternator ideal in weakly alternative rings
zbMATH Open document ID: 0823.17046
DOI: 10.1007/BF02261691
author: R. Kh. Vakhitov
published in: Algebra and Logic
publication date: 1995-04-20T00:00:00Z
review text: Let \(R\) be a ring which satisfies the identity \((x,y,z) = (y,z,x)\) and is without elements of orders 2 and 3 in its additive group. The author proves that \(A^ 2 = 0\), where \(A\) is the alternator ideal of \(R\). In particular, let \(R\) also be a nil ring of bounded index \(n\). Then using results due to Shirshov and Zhevlakov, \(R\) is locally nilpotent; and if \(R\) does not have elements of order \(\leq n\) in its additive group, then \(R\) is solvable of index \(\leq {n(n + 1) \over 2} + 1\).
Mathematics Subject Classification ID: 17D99
zbMATH DE Number: 738947
zbMATH Keywords: weakly alternative rings
zbMATH Keywords: alternator ideal
zbMATH Keywords: nil ring of bounded index
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 738947