6533b7d4fe1ef96bd1261df9
RESEARCH PRODUCT
Specht property for some varieties of Jordan algebras of almost polynomial growth
Lucio CentroneFabrizio MartinoManuela Da Silva Souzasubject
Pure mathematicsPolynomialAlgebra and Number TheoryJordan algebraMathematics::Commutative AlgebraMathematics::Rings and Algebras010102 general mathematicsPolynomial identity specht property Jordan algebra codimensionZero (complex analysis)Triangular matrixField (mathematics)01 natural sciences0103 physical sciences010307 mathematical physicsIdeal (ring theory)Isomorphism0101 mathematicsVariety (universal algebra)Mathematicsdescription
Abstract Let F be a field of characteristic zero. In [25] it was proved that U J 2 , 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 Z 2 -gradings or by a Z 2 × Z 2 -grading. In this paper we prove that the variety of Jordan algebras generated by U J 2 endowed with any G-grading has the Specht property, i.e., every T G -ideal containing the graded identities of U J 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] .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-03-01 |