Hereditary endomorphism rings of mixed Abelian groups

Let $A$ be a finite-rank, torsion-free, self-small mixed abelian $sp$-group and let $E(A)$ be the endomorphism ring of $A$. We give conditions for right and left heredity of $E(A)$. A ring is right hereditary if each of its right ideals is projective. We also find the structure of one-sided ideals of $E(A)$.