Specht property for some varieties of Jordan algebras of almost polynomial growth

Autor(es)

Centrone, Lucio ^[1] ; Martino, Fabrizio ^[1] ; Souza, Manuela da Silva ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Bahia, Dept Matemat, Ave Adhemar de Barros, BR-40170110 Salvador, BA - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 521, p. 137-165, MAR 1 2019.
• Citações Web of Science: 1

Resumo

Let F be a field of characteristic zero. In {[}25] it was proved that UJ(2), the Jordan algebra of 2 x 2 upper triangular matrices, can be endowed up to isomorphism with either the trivial grading or three distinct non-trivial Z(2)-gradings or by a Z(2) x Z(2)-grading. In this paper we prove that the variety of Jordan algebras generated by UJ(2) endowed with any G-grading has the Specht property, i.e., every T-G-ideal containing the graded identities of UJ(2) is finitely based. Moreover, we prove an analogue result about the ordinary identities of A(1), a suitable infinitely generated metabelian Jordan algebra defined in {[}27]. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 18/02108-7 - Identidades em álgebras (não) associativas e temas afins.
• Beneficiário: Lucio Centrone
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 15/08961-5 - Crescimento de álgebras com identidades polinomiais
• Beneficiário: Lucio Centrone
• Modalidade de apoio: Auxílio à Pesquisa - Regular