Ordinal Sums of Projectives in Varieties of Lattices
نویسنده
چکیده
(A for ‘above’; B for ‘below.’) A lattice satisfying this condition is called finitely separable. It is easy to see that every countable lattice is finitely separable. We used this to show the following surprising result: the ordinal sum of two free lattices is projective if and only if one of them is finitely generated or both are countable. In this note we give a complete characterization of when the ordinal sum of two lattices (the lattice obtained by placing the second lattice on top of the first) is projective. This characterization applies not only to the class of all lattices, but to any variety of lattices. In particular, to the class of distributive lattices.
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