Definition:Meet Semilattice/Definition 2

Definition

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

Let $\preceq$ be the ordering on $S$ defined by:

$a \preceq b \iff \paren {a \wedge b} = a$

Then the ordered structure $\struct {S, \wedge, \preceq}$ is called a meet semilattice.

Also see

• Equivalence of Definitions of Meet Semilattice

• Definition:Join Semilattice
• Definition:Semilattice

• Results about meet semilattices can be found here.

Sources

• 1967: Saunders Mac Lane and Garrett Birkhoff: Algebra: Chapter XIV Lattices : $\S 2$ Lattice Identities : Lemma $5$