On the Sum of Two Radical Classes

Let ${\wp}_1$, ${\wp}_2$ be the radical classes of rings. Y. Lee and R. E. Propes have defined their sum by ${\wp}_1+{\wp}_2=\{R{\in}{\omega}:{\wp}_1(R)+{\wp}_2(R)=R\}$. They have shown that ${\wp}_1+{\wp}_2$ is not a radical class in general. In this paper, a few results of Lee and Propes are generalized and also new conditions are investigated under which this sum becomes a radical class.