12 papers · 1 filter
Filters and ideals in pseudocomplemented posets
Ivan Chajda, Helmut Länger
We study ideals and filters of posets and of pseudocomplemented posets and show a version of the Separation Theorem, known for ideals and filters in lattices and semilattices, with…
Extensions and congruences of partial lattices
Ivan Chajda, Helmut Länger
For a partial lattice L the so-called two-point extension is defined in order to extend L to a lattice. We are motivated by the fact that the one-point extension broadly used for p…
Algebras describing pseudocomplemented, relatively pseudocomplemented and sectionally pseudocomplemented posets
Ivan Chajda, Helmut Länger
In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to e…
Sheffer operation in relational systems
Ivan Chajda, Helmut Länger
The concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to e…
Adjoint operations in twist-products of lattices
Ivan Chajda, Helmut Länger
Given an integral commutative residuated lattice L=(L,\vee,\wedge), its full twist-product (L^2,\sqcup,\sqcap) can be endowed with two binary operations \odot and \Rightarrow intro…
Extensions of posets with an antitone involution to residuated structures
Ivan Chajda, Miroslav Kolařík, Helmut Länger
We prove that every not necessarily bounded poset P=(P,\le,') with an antitone involution can be extended to a residuated poset E(P)=(E(P),\le,\odot,\rightarrow,1) where x'=x\right…