Category:Prime Elements

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This category contains results about Prime Elements in the context of Order Theory.


Let $\left({S, \wedge, \preceq}\right)$ be a meet semilattice.

Let $p \in S$.


Then $p$ is prime (element) if and only if

$\forall x, y \in S: \left({ x \wedge y \preceq p \implies x \preceq p \lor y \preceq p }\right)$