Annihilators of Mal'tsev algebras
type: Item
instance of: scholarly article
title: Annihilators of Mal'tsev algebras
zbMATH Open document ID: 0845.17026
DOI: 10.1007/BF00739573
author: V. T. Filippov
published in: Algebra and Logic
publication date: 1996-03-19T00:00:00Z
full work available at URL: https://eudml.org/doc/187701
review text: Let \(\Phi\) be an associative ring with 1, containing \({1\over 6}\), and let \(A\) be a Malcev \(\Phi\)-algebra. Let \[ \{x, y, z\}= (xy)z- (xz)y+ 2x(yz), \] \[ J(x, y, z)= (xy)z+ (zx)y+ (yz)x, \] \[ h(y, z, t, u, x)= u{\textstyle {\partial \over {\partial x}}} \bigl[\{yz, t, x\}x+ \{yx, z, x\}t \bigr]\qquad \text{ and} \] \[ g(y, z, t, v, u, x)= u{\textstyle {\partial\over {\partial x}}} \bigl[J(\{yz, t, x\}, x,v)+ J(\{yx, z, x\}, t, v) \bigr], \] where \(u (\partial/\partial x)\) is the operator of differential substitution \(x\to u\). Let \(G(A) (H(A))\) be the fully invariant ideal of \(A\) generated by \(g(h)\). In the present paper, it is shown that \(G(A) \cdot A^2 \subseteq \text{Ann} (A)\) and that \(H(A) J(A) \subseteq \text{Ann} (A)\). A consequence is that an algebra of characteristic 0 which satisfies the \(n\)-th Engel condition has \(A^n \cdot A^2 \subseteq \text{Ann} (A)\) for some \(n\). These are but a sample of the many such results in this paper.
reviewed by: Ernest L. Stitzinger
Mathematics Subject Classification ID: 17D10
zbMATH DE Number: 848945
zbMATH Keywords: Malcev algebras
zbMATH Keywords: Maltsev algebras
zbMATH Keywords: Engel condition
MaRDI profile type: Publication
cites work: Prime Mal'tsev algebras
cites work: Q3809977
cites work: Malcev Algebras
cites work: The ``measure of non-Lieness'' for Mal'tsev algebras
description: scientific article; zbMATH DE number 848945