Birkhoff: finite distributive lattice ↔ J(P) of down-sets of join-irreducibles

Layer 0 — Mathematicsin the order-theory subtree

Birkhoff 1937 representation theorem — every finite distributive lattice L is isomorphic to the lattice of down-sets of its subposet of join-irreducible elements. More precisely, if JI(L) denotes the poset of join-irreducibles (elements x…

Related concepts

Explore Birkhoff: finite distributive lattice ↔ J(P) of down-sets of join-irreducibles on the interactive knowledge graph →