MATHEMATICA BOHEMICA, Vol. 125, No. 3, pp. 341-354 (2000)

Direct product decompositions of infinitely distributive lattices

Jan Jakubik

Jan Jakubik, Matematicky ustav SAV, Gresakova 6, 040 01 Kosice, Slovakia, e-mail:

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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