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Direct product decompositions of infinitely distributive lattices. (English) Zbl 0967.06004
Summary: Let \(\alpha \) be an infinite cardinal. Let \(\mathcal T_\alpha \) be the class of all lattices which are conditionally \(\alpha \)-complete and infinitely distributive. We denote by \(\mathcal T'_\sigma \) the class of all lattices \(X\) such that \(X\) is infinitely distributive, \(\sigma \)-complete and has the least element. In this paper we deal with direct factors of lattices belonging to \(\mathcal T_\alpha \). As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class \(\mathcal T_\sigma '\).

MSC:
06B23 Complete lattices, completions
06D10 Complete distributivity
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