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].

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 [10.1016/j.jalgebra.2018.11.017].

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

Martino, Fabrizio
;
2019-01-01

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].
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 [10.1016/j.jalgebra.2018.11.017].
File in questo prodotto:
File Dimensione Formato  
Centrone, Martino, Souza, JA, 2019.pdf

Solo gestori archvio

Tipologia: Versione Editoriale
Dimensione 534.11 kB
Formato Adobe PDF
534.11 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/395924
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
social impact