Algebraic lattices

Abbreviation: ALat

Definition

An algebraic lattice is a complete lattice A = (A,∨,∧) such that every element is a join of compact elements.

An element c ∈ A is compact if for every subset S ⊆ A such that c ≤ ∨S, there exists a finite subset S₀ of S such that c ≤ ∨S₀.

Morphisms

Let A and B be algebraic lattices. A morphism from A to B is a function h : A→B that is a complete homomorphism: h(∨S) = ∨h[S] and h(∧S) = ∧h[S].

Some results

Examples

Properties

Subclasses

Superclasses