Partially ordered sets and nonmatrix identities of associative algebras
type: Item
instance of: scholarly article
title: Partially ordered sets and nonmatrix identities of associative algebras
zbMATH Open document ID: 0358.16012
DOI: 10.1007/BF01875930
published in: Algebra and Logic
publication date: 1977-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/186914
review text: In this paper the following theorem including almost all the previous results on Specht's problem is proved. Theorem. Every \(T\)-ideal of the free associative algebra \(F \langle x_1, x_2, \dots \rangle\) over a field \(F\) of characteristic zero containing the polynomial \([x_1,x_2]\dots [x_{2n-1}, x_{2n}]\) finitely generated as \(T\)-ideal. In other words, the variety of all associative algebras satisfying the identity \([x_1,x_2]\dots [x_{2n-1}, x_{2n}] = 0\) satisfies the minimum condition for subvarieties. Corollary 1. Let \(A\) be a finitely generated \(F\)-algebra satisfying the identity which is false on the matrix algebra \(F_2\). Then \(A\) has a finite basis of identities. Corollary 2. The variety generated by the algebra \(F_2\) satisfies the minimum condition for subvarieties.
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16S10
zbMATH DE Number: 3557987
author: Victor N. Latyshev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3557987