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$$z$$-ideals in lattices. (English) Zbl 1438.06008
The authors define $$z$$-ideals in bounded lattices. They establish a separation theorem for the existence of prime $$z$$-ideals in distributive lattices. It follows that in these lattices every $$z$$-ideal is the intersection of some prime $$z$$-ideals. Finally they present a characterization of dually semi-complemented lattices in terms of maximal ideals.
##### MSC:
 06B10 Lattice ideals, congruence relations 06D05 Structure and representation theory of distributive lattices
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