Direct decompositions of non-algebraic complete lattices

Details Direct decompositions of non-algebraic complete lattices Direct decompositions of non-algebraic complete lattices

2005-01-22

arxiv.org/abs/math/0501373v1

Discrete Mathematics 263, Issues 1-3 (2003) 311--321

Mathematics

General Mathematics

Scientific paper

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.

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