How to show that an ideal I of a ring R is semiprimitive if and only if I is an intersection of primitive ideals

Question

A semiprimitive ideal in a ring R is any ideal I such that $J(R/I) = 0$.

I know that for any ring R, the Jacobson radical, $J(R)$, is the intersection of all the left (resp., right) primitive ideals in R.

I don't see how to connect these definitions.

Any help would be great.

Answer 1

The connection is that you can prove $A/I$ is a primitive ideal of $R/I$ iff $A$ is a primitive ideal of $R$ containing $I$.