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On free subalgebras of varieties

Part of: General nonassociative rings Varieties

Published online by Cambridge University Press:  22 November 2021

Renato Fehlberg Júnior Open the ORCID record for Renato Fehlberg Júnior [Opens in a new window]  and
Javier Sánchez Open the ORCID record for Javier Sánchez [Opens in a new window]
Renato Fehlberg Júnior
Affiliation:
Department of Mathematics, Universidade Federal do Espírito Santo, Vitoria, Espírito Santo, Brazil ([email protected])
Javier Sánchez
Affiliation:
Department of Mathematics, IME, University of São Paulo, São Paulo, SP, 05508-090, Brazil ([email protected])
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Abstract

We show that some results of L. Makar-Limanov, P. Malcolmson and Z. Reichstein on the existence of free-associative algebras are valid in the more general context of varieties of algebras.

Keywords

free subalgebrasnon-associative algebrasLie algebrascommutative algebrasanticommutative algebrasspecial Jordan algebrasSchreier varietynon-commutative Poisson algebras

MSC classification

Primary: 17A50: Free algebras
Secondary: 17A01: General theory 17A30: Algebras satisfying other identities 08B20: Free algebras
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 1 , February 2022 , pp. 89 - 101
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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