A variety containing Jordan and pseudo-composition algebras
نویسندگان
چکیده
We consider 3-Jordan algebras, i.e., the nonassociative commutative algebras satisfying (x^3 y)x=x^3(yx). The variety of 3-Jordan algebras contains all Jordan algebras and all pseudo-composition algebras. We prove that a simple 3-Jordan algebra with idempotent is either a Jordan algebra or a pseudo-composition algebra. Disciplines Algebra | Mathematics Comments This article is published as Hentzel, Irvin Roy, and Luiz Antonio Peresi. "A variety containing Jordan and pseudo-composition algebras." East-West Journal of Mathematics 6, no. 1 (2004). Posted with permission. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/math_pubs/134 East-West J. of Mathematics: Vol. 6, No 1 (2004) pp. 67-84 A VARIETY CONTAINING JORDAN AND PSEUDO-COMPOSITION ALGEBRAS Irvin Roy Hentzel∗ and Luiz Antonio Peresi† ∗Department of Mathematics, Iowa State University, Ames, Iowa 50011-2066, U.S.A. e-mail: [email protected] †Departamento de Matemática, Universidade de São Paulo Caixa Postal 66281, São Paulo-SP, Brazil, 05311–970 e-mail: [email protected]
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