Category:Prime Elements

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

Let $\struct {S, \wedge, \preceq}$ be a meet semilattice.

Let $p \in S$.

Then $p$ is a prime element (of $\struct {S, \wedge, \preceq}$) if and only if:

$\forall x, y \in S: \paren {x \wedge y \preceq p \implies x \preceq p \text { or } y \preceq p}$