Boolean and distributive ordered sets: Characterization and representation by sets
- Josef Niederle
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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.
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- Boolean and distributive ordered sets: Characterization and representation by sets
Volume 12, Issue 2 , pp 189-210
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
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- Boolean ordered set
- distributive ordered set
- prime ideal
- maximal ideal
- representation by sets
- Josef Niederle (1)
- Author Affiliations
- 1. Katedra algebry a geometrie přirodovědecké fakulty Masarykovy university, Janáčkovo náměsti 2A, 66295, Brno, Czechia