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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Ring-like operations is pseudocomplemented semilattices

100%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2000
|
tom 20
|
nr 1
87-95
EN
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Orthorings

100%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2004
|
tom 24
|
nr 1
137-147
EN
Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.
3
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Congruence classes in Brouwerian semilattices

100%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2001
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tom 21
|
nr 2
229-237
EN
Brouwerian semilattices are meet-semilattices with 1 in which every element a has a relative pseudocomplement with respect to every element b, i. e. a greatest element c with a∧c ≤ b. Properties of classes of reflexive and compatible binary relations, especially of congruences of such algebras are described and an abstract characterization of congruence classes via ideals is obtained.
4
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Hypersubstitutions in orthomodular lattices

100%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2001
|
tom 21
|
nr 1
83-92
EN
It is shown that in the variety of orthomodular lattices every hypersubstitution respecting all absorption laws either leaves the lattice operations unchanged or interchanges join and meet. Further, in a variety of lattices with an involutory antiautomorphism a semigroup generated by three involutory hypersubstitutions is described.
5
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Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice

100%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2008
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tom 28
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nr 2
251-259
EN
Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.
6
Content available remote

Residuation in orthomodular lattices

100%
Chajda I., Länger H.
Topological Algebra and its Applications
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2017
|
tom 5
|
nr 1
1-5
EN
We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one.
7
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Ring-like structures with unique symmetric difference related to quantum logic

81%
Dorninger D., Länger H., Maczyński M.
Discussiones Mathematicae - General Algebra and Applications
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2001
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tom 21
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nr 2
239-253
EN
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
8
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A generalization of a theorem of Skala

50%
Länger H.
Fundamenta Mathematicae
|
1981
|
tom 112
|
nr 2
121-123
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