an:07091839
Zbl 1438.06008
Joshi, Vinayak; Kavishwar, Shubhangi
$z$-ideals in lattices
EN
Acta Sci. Math. 85, No. 1-2, 59-68 (2019).
00436598
2019
j
06B10 06D05
$z$-ideals; Baer ideal; 0-ideal; closed ideal; minimal prime ideal; maximal ideal; dense ideal; dually semi-complemented lattice
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.
Hans Peter K??nzi (Rondebosch)