4 citations · 13 across the 28 of their papers we have counts for
18 papers · 1 filter
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…
Algebras and varieties where Sasaki operations form an adjoint pair
Ivan Chajda, Helmut Länger
The so-called Sasaki projection was introduced by U. Sasaki on the lattice L(H) of closed linear subspaces of a Hilbert space H as a projection of L(H) onto a certain sublattice of…
Special filters in bounded lattices
Ivan Chajda, Miroslav Kolařík, Helmut Länger
M.S. Rao recently investigated some sorts of special filters in distributive pseudocomplemented lattices. In our paper we extend this study to lattices which need neither be distri…
Implication in weakly and dually weakly orthomodular lattices
Ivan Chajda, Helmut Länger
Weakly orthomodular and dually weakly orthomodular lattices were introduced by the authors in a recent paper. Similarly as for orthomodular lattices we try to introduce an implicat…
c-ideals in complemented posets
Ivan Chajda, Miroslav Kolařík, Helmut Länger
In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension o…
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…
Compositions and decompositions of binary relations
Ivan Chajda, Helmut Länger
It is well-known that to every binary relation on a non-void set I there can be assigned its incidence matrix, also in the case when I is infinite. We show that a certain kind of "…
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…
Semimodular -lattices
Ivan Chajda, Helmut Länger
The concept of a -lattice was introduced by V. Sná\v sel in order to generalize some lattice concepts for directed posets whose elements need not have suprema or infima. We exte…
Semimodules over commutative semirings and modules over unitary commutative rings
Ivan Chajda, Helmut Länger
We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsem…
Sectionally pseudocomplemented posets
Ivan Chajda, Helmut Länger, Jan Paseka
The concept of a sectionally pseudocomplemented lattice was introduced by I. Chajda as an extension of relative pseudocomplementation for not necessarily distributive lattices. The…
On a variety of commutative multiplicatively idempotent semirings
Ivan Chajda, Helmut Länger
We prove that the variety V of commutative multiplicatively idempotent semirings satisfying x + y + xyz = x + y is generated by single semirings. Moreover, we describe a normal for…
Coupled right orthosemirings induced by orthomodular lattices
Ivan Chajda, Helmut Länger
L. P. Belluce, A. Di Nola and B. Gerla established a connection between MV-algebras and (dually) lattice ordered semirings by means of so-called coupled semirings. A similar connec…
General coupled semirings of residuated lattices
Ivan Chajda, Helmut Länger
Di Nola and Gerla showed that MV-algebras and coupled semirings are in a natural one-to-one correspondence. We generalize this correspondence to residuated lattices satisfying the…