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EnglishLet F be a field of characteristic zero. In [25] it was proved that U J2 , the Jordan algebra of 2 × 2 upper triangular matrices, can be endowed up to isomorphism with either the trivial grading or three distinct non-trivial Z2-gradings or by a Z2 × Z2-grading. In this paper we prove that the variety of Jordan algebras generated by UJ2 endowed with any G-grading has the Specht property, i.e., every TG-ideal containing the graded identities of UJ2 is finitely based. Moreover, we prove an analogue result about the ordinary identities of A1, a suitable infinitely generated metabelian Jordan algebra defined in [27].
Centrone, L., Martino, F., & da Silva Souza, M. (2019). Specht property for some varieties of Jordan algebras of almost polynomial growth. JOURNAL OF ALGEBRA, 521, 137-165.
| Data di pubblicazione: | 2019 |
| Titolo: | Specht property for some varieties of Jordan algebras of almost polynomial growth |
| Autori: | |
| Citazione: | Centrone, L., Martino, F., & da Silva Souza, M. (2019). Specht property for some varieties of Jordan algebras of almost polynomial growth. JOURNAL OF ALGEBRA, 521, 137-165. |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jalgebra.2018.11.017 |
| Abstract: | Let F be a field of characteristic zero. In [25] it was proved that U J2 , the Jordan algebra of 2 × 2 upper triangular matrices, can be endowed up to isomorphism with either the trivial grading or three distinct non-trivial Z2-gradings or by a Z2 × Z2-grading. In this paper we prove that the variety of Jordan algebras generated by UJ2 endowed with any G-grading has the Specht property, i.e., every TG-ideal containing the graded identities of UJ2 is finitely based. Moreover, we prove an analogue result about the ordinary identities of A1, a suitable infinitely generated metabelian Jordan algebra defined in [27]. |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/10447/395924
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