Hereditary radicals in Jordan rings

Abstract:

The object of this paper is to examine some radical properties of quadratic Jordan algebras and to show that under certain conditions, $R(\mathfrak {B}) = \mathfrak {B} \cap R(\mathfrak {J})$ where $\mathfrak {B}$ is an ideal of a quadratic Jordan algebra $\mathfrak {J},R(\mathfrak {B})$ is the radical of $\mathfrak {B}$, and $R(\mathfrak {J})$ is the radical of $\mathfrak {J}$.