Free Akivis algebras, primitive elements, and hyperalgebras
type: Item
instance of: scholarly article
title: Free Akivis algebras, primitive elements, and hyperalgebras
zbMATH Open document ID: 0993.17002
author: Ivan Shestakov
author: Ualbai Umirbaev
published in: Journal of Algebra
publication date: 2002-07-04T00:00:00Z
review text: The notions of free Akivis algebra, its enveloping algebra, and its primitive element are given. It is proved that subalgebras of a free Akivis algebra are also free and finitely generated subalgebras are finitely residual. Decidability of the word problem for the variety of Akivis algebras is also proved. It is proved that a set of multilinear operations can be constructed for every algebra \(B\) such that \(B\) becomes a hyperalgebra called \(G(B)\). The following problem is stated: is it true that any hyperalgebra can be isomorphically embedded into a hyperalgebra \(G(B)\) for a suitable algebra \(B\)?
Mathematics Subject Classification ID: 17A50
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 1763545
zbMATH Keywords: Akivis algebra
zbMATH Keywords: free Akivis algebra
zbMATH Keywords: hyperalgebra
zbMATH Keywords: primitive element
zbMATH Keywords: loop
zbMATH Keywords: decidability
reviewed by: A. M. Shelekhov
MaRDI profile type: Publication
OpenAlex ID: W2034062601
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DOI: 10.1006/JABR.2001.9123
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description: scientific article; zbMATH DE number 1763545