Direct decompositions of non-algebraic complete lattices

Friedrich Wehrung (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

For a given complete lattice L, we investigate whether L can be decomposed as a direct product of directly indecomposable lattices. We prove that this is the case if every element of L is a join of join-irreducible elements and dually, thus extending to non-algebraic lattices a result of L. Libkin. We illustrate this by various examples and counterexamples.

Mots clés: spatial; complete; lattice; center; direct product; directly indecomposable; join-irreducible; spatial.

Domaines: Mathématiques générales [math.GM]

Friedrich Wehrung. Direct decompositions of non-algebraic complete lattices. Discrete Mathematics, 2003, 263 (1--3), pp.311-321. ⟨10.1016/S0012-365X(02)00790-2⟩. ⟨hal-00004019⟩