Finite-dimensional right alternative algebras that do not generate finitely based varieties
type: Item
instance of: scholarly article
title: Finite-dimensional right alternative algebras that do not generate finitely based varieties
zbMATH Open document ID: 0618.17010
DOI: 10.1007/BF01978883
author: I. M. Isaev
published in: Algebra and Logic
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187343
review text: The class of right-alternative algebras is defined by the following two identities: \((xy)y=xy^ 2,\quad ((xy)z)y=x((yz)y).\) It is known [\textit{I. V. L'vov}, Algebra Logika 17, No.3, 282-286 (1978; Zbl 0414.17009)] that any finite alternative algebra has a finite basis of identities. An example of a finite dimensional right-alternative algebra over an arbitrary field which has not any finite basis of identities is constructed. This one gives a negative answer to the corresponding question posed by \textit{I. V. L'vov} [in Dnestrovskaya tetrad', Novosibirsk (1982; Zbl 0493.16001)].
Mathematics Subject Classification ID: 17D15
zbMATH DE Number: 4002340
zbMATH Keywords: varieties of right-alternative algebras without finite basis of identities
reviewed by: Grigori I. Zhitomirski
MaRDI profile type: Publication
cites work: Q3947798
cites work: Q4132696
cites work: Q4168728
OpenAlex ID: W1980856650
description: scientific article; zbMATH DE number 4002340