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

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.

### MSC:

 06A12 Semilattices