On \(n\)-normal posets (Q539193)

The authors introduce the notion of \(n\)-normality for partially ordered sets. Thus, a poset is said to be \(n\)-normal provided that every of its prime ideals contains at most \(n\) prime ideals. Matching this new concept and the prime ideal theorem for finite ideal distributive posets, the authors describe the main properties of \(n\)-normal posets, and characterize them among finite ideal-distributive posets thus generalizing a result by \textit{W. H. Cornish} [``\(n\)-normal lattices'', Proc. Am. Math. Soc. 45, 48--54 (1974; Zbl 0294.06008)].