Clanek podava přehled o nejdůležitějsich aktualnich výsledcich týkajicich se tzv. diofantovských ... more Clanek podava přehled o nejdůležitějsich aktualnich výsledcich týkajicich se tzv. diofantovských n -tic. Obsahuje definici diofantovske n -tice a je v něm diskutovana mj. take existence tzv. diofantovských pětic.
The couple of numbers p , p + 2, where both are prime, is called a prime twin. The problem if the... more The couple of numbers p , p + 2, where both are prime, is called a prime twin. The problem if there exists an infinite number of prime twins is not already solved and no method how to solve it is known. Due to this it is considered to be a breakdown the newest result by Y. Zhang proving the existence of a natural number b such that there exists an infinite number of couples of primes p , p + b . Unfortunately, the smallest estimation for this b is 70 milliards.
Skew effect algebras were already introduced as a non-associative modification of the so-called e... more Skew effect algebras were already introduced as a non-associative modification of the so-called effect algebras which serve as an algebraic axiomatization of the propositional logic of quantum mechanics. Since skew effect algebras have a partial binary operation, we search for an algebra with a total binary operation which extends a given skew effect algebra and such that the underlying posets coincide. It turns out that the suitable candidate is a skew basic algebra. Algebraic properties of skew basic algebras are described and they are compared with the so-called pseudo basic algebras introduced by the authors recently.
Paraorthomodular lattices are quantum structures of prominent importance within the framework of ... more Paraorthomodular lattices are quantum structures of prominent importance within the framework of the logico-algebraic approach to (unsharp) quantum theory. However, at the present time it is not clear whether the above algebras may be regarded as the algebraic semantic of a logic in its own right. In this paper, we start the investigation of material implications in paraorthomodular lattices by showing that any bounded modular lattice with antitone involution $${\\mathbf {A}}$$ A can be converted into a left-residuated groupoid if it satisfies a strengthened form of regularity. Moreover, the above condition turns out to be also necessary whenever $${\\mathbf {A}}$$ A is distributive.
Clanek podava přehled o nejdůležitějsich aktualnich výsledcich týkajicich se tzv. diofantovských ... more Clanek podava přehled o nejdůležitějsich aktualnich výsledcich týkajicich se tzv. diofantovských n -tic. Obsahuje definici diofantovske n -tice a je v něm diskutovana mj. take existence tzv. diofantovských pětic.
The couple of numbers p , p + 2, where both are prime, is called a prime twin. The problem if the... more The couple of numbers p , p + 2, where both are prime, is called a prime twin. The problem if there exists an infinite number of prime twins is not already solved and no method how to solve it is known. Due to this it is considered to be a breakdown the newest result by Y. Zhang proving the existence of a natural number b such that there exists an infinite number of couples of primes p , p + b . Unfortunately, the smallest estimation for this b is 70 milliards.
Skew effect algebras were already introduced as a non-associative modification of the so-called e... more Skew effect algebras were already introduced as a non-associative modification of the so-called effect algebras which serve as an algebraic axiomatization of the propositional logic of quantum mechanics. Since skew effect algebras have a partial binary operation, we search for an algebra with a total binary operation which extends a given skew effect algebra and such that the underlying posets coincide. It turns out that the suitable candidate is a skew basic algebra. Algebraic properties of skew basic algebras are described and they are compared with the so-called pseudo basic algebras introduced by the authors recently.
Paraorthomodular lattices are quantum structures of prominent importance within the framework of ... more Paraorthomodular lattices are quantum structures of prominent importance within the framework of the logico-algebraic approach to (unsharp) quantum theory. However, at the present time it is not clear whether the above algebras may be regarded as the algebraic semantic of a logic in its own right. In this paper, we start the investigation of material implications in paraorthomodular lattices by showing that any bounded modular lattice with antitone involution $${\\mathbf {A}}$$ A can be converted into a left-residuated groupoid if it satisfies a strengthened form of regularity. Moreover, the above condition turns out to be also necessary whenever $${\\mathbf {A}}$$ A is distributive.
We study so-called near semirings endowed with an antitone involution. Such a near semiring is in... more We study so-called near semirings endowed with an antitone involution. Such a near semiring is in fact a bounded lattice which has one more binary operation, the multiplication. We classify several families of bounded lattices which can be organized in such near semirings, e.g. chains or orthomodular lattices. A particular case are the so-called balanced near semirings which form a variety which is congruence distributive, permutable and regular.
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Papers by Ivan Chajda