6 papers · 1 filter
Operators on complemented posets
Michal Botur, Ivan Chajda, Helmut Länger
Given a complemented poset P, we can assign to every element x of P the set x^+ of all its complements. We study properties of the operator ^+ on P, in particular, we are intereste…
Lagrange-like interpolation in unitary rings, Boolean algebras and Boolean posets
Ivan Chajda, Helmut Länger
It is known that every function with a finite support over a given field can be interpolated by means of the Lagrangian polynomial. The question is if a similar interpolation is po…
Properties of the symmetric difference in lattices with complementation
Václav Cenker, Ivan Chajda, Helmut Länger
The symmetric difference in Boolean lattices can be defined in two different but equivalent forms. However, it can be introduced also in every bounded lattice with complementation…
Operators Max L and Min U and duals of Boolean posets
Ivan Chajda, Miroslav Kolařík, Helmut Länger
When working with posets which are not necessarily lattices, one has a lack of lattice operations which causes problems in algebraic constructions. This is the reason why we use th…
Congruences on posets, relatively pseudocomplemented and Boolean posets
Ivan Chajda, Helmut Länger
The aim of the present paper is to extend the concept of a congruence from lattices to posets. We use an approach different from that used by the first author and V. Snášel. By usi…
Derived operators on skew orthomodular and strong skew orthomodular posets
Ivan Chajda, Helmut Länger
It is well-known that in the logic of quantum mechanics disjunctions and conjunctions can be represented by joins and meets, respectively, in an orthomodular lattice provided their…