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

JOURNAL OF ALGEBRA

卷:521

Article

Centrone, Lucio¹  Martino, Fabrizio¹  Souza, Manuela da Silva² 

[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

关键词: Polynomial identity;    Jordan algebra;    Specht property;    Growth;    Codimension;   

DOI  :  10.1016/j.jalgebra.2018.11.017

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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