Definition:Prime Element (Order Theory)/Lattice

Definition

Let $L = \struct{S, \vee, \wedge, \preceq}$ be a lattice.

Let $z \in S$.

Then $z$ is said to be meet prime element in L if and only if

$z$ is a prime element in the meet semilattice $\struct{S, \wedge, \preceq}$

Also defined as

The term meet prime is sometimes hyphenated as meet-prime in some sources.

Also see

• Definition:Join Prime Element (Lattice)

• Definition:Meet Irreducible Element (Lattice)

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.