Identities of sums of commutative subalgebras
type: Item
instance of: scholarly article
title: Identities of sums of commutative subalgebras
zbMATH Open document ID: 0829.16014
DOI: 10.1007/BF02844841
author: Antonio Giambruno
author: Yuri Bahturin
publication date: 1995-08-10T00:00:00Z
review text: \textit{N. Itô} [Math. Z. 62, 400-401 (1955; Zbl 0064.25203)] proved that a group which is a product of two abelian subgroups is metabelian, i.e. 2-step solvable, and this result has stimulated investigations in similar spirit for Lie and associative algebras. In the paper under review the authors give a short and straightforward proof that if a ring \(R\) is a sum of two commutative subrings then \(R\) satisfies the polynomial identity \([x,y][z,t]=0\). They also establish that this identity is minimal, i.e. determines the variety of associative rings generated by all rings presented as sums of two commutative subrings. Recently [\textit{Yu. Bakhturin} and \textit{O. H. Kegel}, Commun. Algebra 23, 2975-2990 (1995; Zbl 0837.16020)] these results were generalized for superalgebras.
reviewed by: Vesselin Drensky
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 16R40
zbMATH DE Number: 760329
zbMATH Keywords: sums of commutative subrings
zbMATH Keywords: polynomial identities
zbMATH Keywords: varieties of associative rings
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02844841
OpenAlex ID: W2008460602
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 760329