Definition:Meet Semilattice/Definition 2
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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
- 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 $5$