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Direct decompositions of non-algebraic complete lattices

Friedrich Wehrung
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Abstract

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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Friedrich Wehrung. 2005-01-22. Direct decompositions of non-algebraic complete lattices. https://arxiv.org/abs/math/0501373

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