## The ordinal variety of distributive ordered sets of width two.(English)Zbl 0773.06006

An ordered set $$P$$ is said to be distributive if $$L(U(a,b),c)=LU(L(a,c),L(b,c))$$, where $$L(X)$$ and $$U(X)$$ denote the sets of all lower and upper bounds of a subset $$X$$ in $$P$$ respectively. The author looks for ordinally irreducible distributive ordered sets of width two.
Reviewer: J.Niederle (Brno)

### MSC:

 06A07 Combinatorics of partially ordered sets

### Keywords:

distributivity; ordinally irreducible ordered set

### References:

 [1] Chajda I., Rachůnek J.: Forbidden configurations for distributive and modular ordered sets. Order 5 (1989), 407-423. · Zbl 0674.06003 [2] Duffus D., Rival I.: A structure theory for ordered sets. Discrete Math. 35 (1981), 53-118. · Zbl 0459.06002 [3] Larmerová J., Rachůnek J.: Translations of distributive and modular ordered sets. Acta Univ.Palack. Olomucensis, Fac. Rer. Nat. Math. 91 (1988), 13-23. · Zbl 0693.06003 [4] Rachůnek J.: Ordinal varieties of ordered sets. · Zbl 0736.06008 [5] Skornjakov L.A.: Elements of Lattice Theory. (Russian), Nauka, Moscow, 1970. · Zbl 0312.16020
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