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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 1, Pages 185–197
DOI: https://doi.org/10.33048/smzh.2021.62.116 (Mi smj7548) 		 
Nilpotency of alternative and Jordan algebras

A. V. Popov

Ulyanovsk State University, Ulyanovsk, Russia
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DOI: https://doi.org/10.33048/smzh.2021.62.116
Abstract: We study the polynomial identities of alternative and Jordan algebras which imply the nilpotency of the algebras. In the case of a field of characteristic 0 we describe all these systems of identities as well as all almost nilpotent varieties of alternative and Jordan algebras. In particular, we establish a connection between the Engel identity for the Lie algebras and the standard identity for the Jordan algebras.
Keywords: Jordan algebras, alternative algebras, almost nilpotent varieties, Nagata–Higman Theorem, Engel identity, standard Jordan identity.
Received: 16.06.2020
Revised: 16.06.2020
Accepted: 09.10.2020
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 1, Pages 148–158
DOI: https://doi.org/10.1134/S003744662101016X
Bibliographic databases:
Document Type: Article
UDC: 512.554.5+7
Language: Russian
Citation: A. V. Popov, “Nilpotency of alternative and Jordan algebras”, Sibirsk. Mat. Zh., 62:1 (2021), 185–197; Siberian Math. J., 62:1 (2021), 148–158
Citation in format AMSBIB
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