Definition:Prime Ideal of Ring

Definition
Let $$\left({R, +, \circ}\right)$$ be a ring.

Let $$J$$ be an ideal of $$R$$.

Then $$J$$ is a prime ideal iff:
 * $$J_1 \circ J_2 \subseteq J \implies J_1 \subseteq J \text{ or } J_2 \subseteq J$$

for any ideals $$J_1$$ and $$J_2$$ of $$R$$.