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MATHEMATICA BOHEMICA, Vol. 125, No. 3, pp. 341-354 (2000)
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# Direct product decompositions of infinitely distributive lattices

## Jan Jakubik

* Jan Jakubik*, Matematicky ustav SAV, Gresakova 6, 040 01 Kosice, Slovakia, e-mail: ` musavke@mail.saske.sk`

**Abstract:**
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 $\Cal T_\sigma '$.

**Keywords:** direct product decomposition, infinite distributivity, conditional $\alpha$-completeness

**Classification (MSC2000):** 06B35, 06D10

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