Definition:Completely Prime Ideal

Definition

Let $\struct{S, \preceq}$ be an ordered set.

Let $I$ be a proper ideal in $\struct{S, \preceq}$.

$I$ is a completely prime ideal if and only if:

$\forall J \subseteq S: \paren{\inf J \in I \implies I \cap J \ne \O }$

Also see

• Definition:Completely Prime Filter

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