On the Bar-radical of Jordan Baric Algebras

Abstract.

In this paper, we prove that if (U, w) is a finite dimensional Jordan baric algebra such that $\text{rad}(U)\subseteq(\text{bar}(U))^3$ then, $\text{rad}(U)=R(U)\cap(\text{bar}(U))^3$, where R(U) is the nilradical (maximal nil ideal) of U. We also give conditions so that $\text{rad}(U)\subseteq (\text{bar}(U))^3$ and an example showing that such conditions are necessary.