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Rachůnek, J.

A characterization of \(o\)-distributive semilattices. (English) Zbl 0736.06008

Acta Sci. Math. 54, No. 3-4, 241-246 (1990).

The paper deals with a generalization of distributive semilattices, namely semilattices which are distributive as ordered sets, i.e. ordered sets for which the distributive law holds if joins (meets) are taken in the lattice of order ideals (filters). It is shown that the failure of this property implies the occurrence of one out of a list of four small non-distributive subsemilattices.

Reviewer: C.Herrmann (Darmstadt)

Cited in 4 Documents

MSC:

06A12

Semilattices

Keywords:

generalization of distributive semilattices; order ideals

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