Basic superranks for varieties of algebras

Autor(es)

Kuz'min, Alexey ; Shestakov, Ivan

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 478, p. 58-91, MAY 15 2017.
• Citações Web of Science: 0

Resumo

We introduce the notion of basic superrank for varieties of algebras generalizing the notion of basic rank. First we consider a number of varieties of nearly associative algebras over a field of characteristic 0 that have infinite basic ranks and calculate their basic superranks which turns out to be finite. Namely we prove that the variety of alternative metabelian (solvable of index 2) algebras possesses the two basic superranks (1,1) and (0,3); the varieties of Jordan and Malcev metabelian algebras have the unique basic superranks (0,2) and (1,1), respectively. Furthermore, for arbitrary pair (r, s) not equal (0,0) of nonnegative integers we provide a variety that has the unique basic superrank (r, s). Finally, we construct some examples of nearly associative varieties that do not possess finite basic superranks. (C) 2017 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 10/51880-2 - On finite basis property for varieties of nearly associative algebras.
• Beneficiário: Alexey Kuzmin
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado