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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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