What is the meaning of Prime_ideal?

Any (two-sided) ideal $I$ such that for arbitrary ideals $P$ and $Q$ , $P Q \subseteq I ⟹ P \subseteq I$ or $Q \subseteq I$ .

In a commutative ring, a (two-sided) ideal $I$ such that for arbitrary ring elements $a$ and $b$ , $a b \in I ⟹ a \in I$ or $b \in I$ .

Source: wiktionary.org