Jakubík, Ján Direct product decompositions of infinitely distributive lattices. (English) Zbl 0967.06004 Math. Bohem. 125, No. 3, 341-354 (2000). 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 \(\mathcal T_\sigma '\). Cited in 2 Documents MSC: 06B23 Complete lattices, completions 06D10 Complete distributivity Keywords:direct product decomposition; infinite distributivity; conditional \(\alpha \)-completeness PDFBibTeX XMLCite \textit{J. Jakubík}, Math. Bohem. 125, No. 3, 341--354 (2000; Zbl 0967.06004) Full Text: EuDML