# Article

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Keywords:
direct product decomposition; infinite distributivity; conditional $\alpha$-completeness
Summary:
Let $\alpha$ be an infinite cardinal. Let $\Cal T_\alpha$ be the class of all lattices which are conditionally $\alpha$-complete and infinitely distributive. We denote by $\Cal{T}_\sigma'$ 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 $\Cal T_\alpha$. As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class $\Cal T_\sigma'$.
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