Article ID Journal Published Year Pages File Type
4586487 Journal of Algebra 2011 11 Pages PDF
Abstract

We show that in Jordan systems (algebras, triple systems, and pairs) monomials containing two elements of a trivial minimal ideal vanish, so improving the answer given by Anquela and Cortés in [J.A. Anquela, T. Cortés, Minimal ideals of Jordan systems, Invent. Math. 168 (2007) 83–90] to the problem of Nam and McCrimmon in [N.S. Nam, K. McCrimmon, Minimal ideals in quadratic Jordan algebras, Proc. Amer. Math. Soc. 88 (4) (1983) 579–583], inspired by the problem posed in 1971 by Zhevlakov in the Dniester Notebook: Unsolved Problems in the Theory of Rings and Modules (second ed., 1976) (see Filippov et al. (1993) [5]).

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory