, Volume 12, Issue 2, pp 189-210

First online:

Boolean and distributive ordered sets: Characterization and representation by sets

  • Josef NiederleAffiliated withKatedra algebry a geometrie přirodovědecké fakulty Masarykovy university

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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 set distributive ordered set ideal prime ideal maximal ideal representation by sets