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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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On GE-algebras

100%
Bandaru R., Saeid A. B., Jun Y. B.
Bulletin of the Section of Logic
|
2021
|
tom 50
|
nr 1
81-96
EN
Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.
2
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Implication algebras

88%
Chajda I.
Discussiones Mathematicae - General Algebra and Applications
|
2006
|
tom 26
|
nr 2
141-153
EN
We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties.
3
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Distributive implication groupoids

88%
Chajda I., Halaš R.
Open Mathematics
|
2007
|
tom 5
|
nr 3
484-492
EN
We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.
4
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Ring-like operations is pseudocomplemented semilattices

75%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2000
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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.
5
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Congruences on semilattices with section antitone involutions

75%
Chajda I.
Discussiones Mathematicae - General Algebra and Applications
|
2010
|
tom 30
|
nr 2
207-215
EN
We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.
6
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Orthorings

63%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2004
|
tom 24
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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.
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