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Start Over Creator Halaš, Radomír

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

Creator:
Halaš, Radomír and Hort, Daniel
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
ordered sets and morphisms
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Annihilators in BCK-algebras

Creator:
Halaš, Radomír
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
BCK-algebra, deductive system, annihilator, and pseudocomplement
Language:
English
Description:
We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra $\mathcal A$. We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice $\mathcal D (A)$ of all deductive systems on $\mathcal A$. Moreover, relative annihilators of $C\in \mathcal D (A)$ with respect to $B \in \mathcal D (A)$ are introduced and serve as relative pseudocomplements of $C$ w.r.t. $B$ in $\mathcal D (A)$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Normalization of MV -algebras

Creator:
Chajda, Ivan, Halaš, Radomír, Kühr, Jan, and Vanžurová, Alena
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
MV -algebra, abelian lattice-ordered group, q-lattice, and normalization of a variet
Language:
English
Description:
We consider algebras determined by all normal identities of MV -algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a q-lattice, and another one based on a normalization of a lattice-ordered group.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. On systems of congruences on principal filters of orthomodular implication algebras

Creator:
Halaš, Radomír and Plojhar, Luboš
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
orthoimplication algebra, orthomodular lattice, and p-filter
Language:
English
Description:
Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott’s implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

6. Relative polars in ordered sets

Creator:
Halaš, Radomír
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
ordered set, distributive set, ideal, prime ideal, $R$-polar, and annihilator
Language:
English
Description:
In the paper, the notion of relative polarity in ordered sets is introduced and the lattices of $R$-polars are studied. Connections between $R$-polars and prime ideals, especially in distributive sets, are found.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

7. Subdirectly irreducible sectionally pseudocomplemented semilattices

Creator:
Halaš, Radomír and Kühr, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
sectionally pseudocomplemented semilattice and weakly standard element
Language:
English
Description:
Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented semilattices.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public