Power-associative algebras that are train algebras
type: Item
instance of: scholarly article
title: Power-associative algebras that are train algebras
zbMATH Open document ID: 1230.17027
author: Joseph Bayara
author: André Conseibo
author: Moussa Ouattara
author: Fouad Zitan
published in: Journal of Algebra
publication date: 2011-01-07T00:00:00Z
review text: The authors investigate the structure of power-associative algebras which also are train algebras. In particular: -- The train equation of such an algebra is determined. -- In the finite-dimensional case, it is shown that the dimensions of the Peirce components are invariant and that the upper bounds for their nil-indexes are reached for some idempotent. -- It is shown that locally train algebras are, in fact, train algebras. Moreover, the set of idempotents is studied in detail and special attention is paid to the Jordan and Bernstein cases.
Mathematics Subject Classification ID: 17D92
Mathematics Subject Classification ID: 17A05
zbMATH DE Number: 5833414
zbMATH Keywords: absolutely primitive idempotent
zbMATH Keywords: Bernstein algebra
zbMATH Keywords: Jordan algebra
zbMATH Keywords: Peirce decomposition
zbMATH Keywords: principal idempotent
zbMATH Keywords: power-associative algebra
zbMATH Keywords: stable algebra
zbMATH Keywords: train algebra
reviewed by: Antonio M. Oller Marcén
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.06.012
OpenAlex ID: W2103730278
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DOI: 10.1016/J.JALGEBRA.2010.06.012
description: scientific article; zbMATH DE number 5833414