25 citations · 39 across the 40 of their papers we have counts for
19 papers · 1 filter
Lattices and semilattices derived from commutative rings of characteristic 2 satisfying the identity
Ivan Chajda, Miroslav Kolařík, Helmut Länger
We prove that a commutative ring of characteristic satisfying the identity together with the binary relation on defined by…
Varieties and quasivarieties of lattices with complementation
V. Cenker, I. Chajda, J. Kühr +1
We investigate (quasi)varieties of lattices with complementation, i.e., complemented lattices equipped with a fixed complementation as a unary operation. We focus on subclasses sat…
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…
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…
Adjointness of generalized Sasaki operations in posets
Ivan Chajda, Helmut Länger
The Sasaki projection and its dual were introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. In a previous paper the authors sh…
Quasimodules over bounded lattices
Ivan Chajda, Helmut Länger
We define a quasimodule Q over a bounded lattice L in an analogous way as a module over a semiring is defined. The essential difference is that L need not be distributive. Also for…
The operator of relative complementation
Ivan Chajda, Helmut Länger
By the operator of relative complementation is meant a mapping assigning to every element x of an interval [a,b] of a lattice L the set x^{ab} of all relative complements of x in […
Properties and special filters of pseudocomplemented posets
Ivan Chajda, Helmut Länger
Investigating the structure of pseudocomplemented lattices started ninety years ago with papers by V. Glivenko, G. Birkhoff and O. Frink and this structure was essentially develope…
Remarks on special congruences
Ivan Chajda, Helmut Länger
We study algebras and varieties where every non-trivial congruence has some class being a non-trivial subuniverse of the algebra in question. Then we focus on algebras where this n…
Integration in semirings
Ivan Chajda, Helmut Länger
The concept of integral as an inverse to that of derivation was already introduced for rings and recently also for lattices. Since semirings generalize both rings and bounded distr…
Residuation in twist products and pseudo-Kleene posets Abstract
Ivan Chajda, Helmut Länger
M. Busaniche, R. Cignoli, C. Tsinakis and A. M. Wille showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also la…
Kleene posets and pseudo-Kleene posets
Ivan Chajda, Helmut Länger
The concept of a Kleene algebra (sometimes also called Kleene lattice) was already generalized by the first author for non-distributive lattices under the name pseudo-Kleene algebr…
Sublattices and -blocks of orthomodular posets
Ivan Chajda, Helmut Länger
For orthoposets we introduce a binary relation Delta and a binary operator d(x,y) which are generalizations of the binary relation C and the commutator c(x,y), respectively, known…
Orthogonality and complementation in the lattice of subspaces of a finite-dimensional vector space over a finite field
Ivan Chajda, Helmut Länger
We investigate the lattice L(V) of subspaces of an m-dimensional vector space V over a finite field GF(q) with q being the n-th power of a prime p. It is well-known that this latti…
Varieties corresponding to classes of complemented posets
Ivan Chajda, Miroslav Kolařík, Helmut Länger
As algebraic semantics of the logic of quantum mechanics there are usually used orthomodular posets, i.e. bounded posets with a complementation which is an antitone involution and…
Ideals of direct products of rings
Ivan Chajda, Günther Eigenthaler, Helmut Länger
It is known that an ideal of a direct product of commutative unitary rings is directly decomposable into ideals of the corresponding factors. We show that this does not hold in gen…
Directly decomposable ideals and congruence kernels of commutative semirings
Ivan Chajda, Günther Eigenthaler, Helmut Länger
As pointed out in the monographs by J. S. Golan and by W. Kuich and A. Salomaa on semirings, ideals play an important role despite the fact that they need not be congruence kernels…
Orthomodular lattices can be converted into left residuated l-groupoids
Ivan Chajda, Helmut Länger
We show that every orthomodular lattice can be considered as a left residuated l-groupoid satisfying divisibility, antitony, the double negation law and three more additional condi…
When does a semiring become a residuated lattice?
Ivan Chajda, Helmut Länger
It is an easy observation that every residuated lattice is in fact a semiring because multiplication distributes over join and the other axioms of a semiring are satisfied triviall…