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A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets

Radomír Halaš, Daniel Hort (2003)

Czechoslovak Mathematical Journal

We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.

A characterization of finite Stone pseudocomplemented ordered sets

Radomír Halaš (1996)

Mathematica Bohemica

A distributive pseudocomplemented set S [2] is called Stone if for all a ∈ S the condition L U ( a * , a * * ) = S holds. It is shown that in a finite case S is Stone iff the join of all distinct minimal prime ideals of S is equal to S .

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