What is the meaning of Prime_ideal?

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

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

Source: wiktionary.org

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