×

zbMATH — the first resource for mathematics

\(z\)-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
PDF BibTeX XML Cite
Full Text: DOI