, Volume 12, Issue 2, pp 189–210

Boolean and distributive ordered sets: Characterization and representation by sets

  • Josef Niederle

DOI: 10.1007/BF01108627

Cite this article as:
Niederle, J. Order (1995) 12: 189. doi:10.1007/BF01108627


Boolean ordered sets generalize Boolean lattices, and distributive ordered sets generalize distributive lattices. Ideals, prime ideals, and maximal ideals in ordered sets are defined, and some well-known theorems on Boolean lattices, such as the Glivenko-Stone theorem and the Stone representation theorem, are generalized to Boolean ordered sets. A prime ideal theorem for distributive ordered sets is formulated, and the Birkhoff representation theorem is generalized to distributive ordered sets. Fundamental are the embedding theorems for Boolean ordered sets and for distributive ordered sets.

Mathematics Subject Classification (1991)


Key words

Boolean ordered setdistributive ordered setidealprime idealmaximal idealrepresentation by sets

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Josef Niederle
    • 1
  1. 1.Katedra algebry a geometrie přirodovědecké fakulty Masarykovy universityBrnoCzechia