Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 1

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Definition

Let $\struct {R, +, \circ}$ be a commutative and unitary ring.


A prime ideal of $R$ is a proper ideal $P$ such that:

$\forall a, b \in R : a \circ b \in P \implies a \in P$ or $b \in P$


Also see