  We show that every finite semilattice can be represented as an atomized
semilattice, an algebraic structure with additional elements (atoms) that
extend the semilattice's partial order. Each atom maps to one subdirectly
irreducible component, and the set of atoms forms a hypergraph that fully
defines the semilattice. An atomization always exists and is unique up to
"redundant atoms". Atomized semilattices are representations that can be used
as computational tools for building semilattice models from sentences, as well
as building its subalgebras and products. Atomized semilattices can be applied
to machine learning and to the study of semantic embeddings into algebras with
idempotent operators.
