\(z\)-ideals in lattices. (English) Zbl 1438.06008

Joshi, Vinayak; Kavishwar, Shubhangi

Acta Sci. Math. 85, No. 1-2, 59-68 (2019).

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.

Reviewer: Hans Peter Künzi (Rondebosch)

MSC:

06B10	Lattice ideals, congruence relations
06D05	Structure and representation theory of distributive lattices

Keywords:

\(z\)-ideals; Baer ideal; 0-ideal; closed ideal; minimal prime ideal; maximal ideal; dense ideal; dually semi-complemented lattice