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Wyświetlanie 1-15 z 52
Tytuł:
On the Leibniz congruences
Autorzy:
Font, Josep
Powiązania:
https://bibliotekanauki.pl/articles/1361077.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
deductive system
protoalgebraic logic
Gentzen calculus
closure operator
abstract logic
algebraizable logic
Leibniz congruence
selfextensional logic
logical matrices
algebraic logic
Opis:
The aim of this paper is to discuss the motivation for a new general algebraic semantics for deductive systems, to introduce it, and to present an outline of its main features. Some tools from the theory of abstract logics are also introduced, and two classifications of deductive systems are analysed: one is based on the behaviour of the Leibniz congruence (the maximum congruence of a logical matrix) and the other on the behaviour of the Frege operator (which associates to every theory the interderivability relation modulo the theory). For protoalgebraic deductive systems the class of algebras associated in general turns out to be the class of algebra reducts of reduced matrices, which is the algebraic counterpart usually considered for this large class of deductive systems; but in the general case the new class of algebras shows a better behaviour.
Źródło:
Banach Center Publications; 1993, 28, 1; 17-36
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Congruence lattices of free lattices in non-distributive varieties
Autorzy:
Ploščica, Miroslav
Tůma, Jiří
Wehrung, Friedrich
Powiązania:
https://bibliotekanauki.pl/articles/966045.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
diamond
congruence splitting lattice
Kuratowski's Theorem
Uniform Refinement Property
congruence lattice
pentagon
Źródło:
Colloquium Mathematicum; 1998, 76, 2; 269-278
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Congruences on pseudocomplemented semilattices
Autorzy:
Heleyová, Zuzana
Powiązania:
https://bibliotekanauki.pl/articles/728824.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
pseudocomplemented semilattice
congruence lattice
p-algebra
Stone algebra
(relative) (Lₙ)-lattice
Opis:
It is known that congruence lattices of pseudocomplemented semilattices are pseudocomplemented [4]. Many interesting properties of congruences on pseudocomplemented semilattices were described by Sankappanavar in [4], [5], [6]. Except for other results he described congruence distributive pseudocomplemented semilattices [6] and he characterized pseudocomplemented semilattices whose congruence lattices are Stone, i.e. belong to the variety B₁ [5].
In this paper we give a partial solution to a more general question: Under what condition on a pseudocomplemented semilattice its congruence lattice is element of the variety Bₙ (n ≥ 2)?
In the last section we widen the Sankappanavar's result to obtain the description of pseudocomplemented semilattices with relative Stone congruence lattices. A partial solution of the description of pseudocomplemented semilattices with relative (Lₙ)-congruence lattices (n ≥ 2) is also given.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 219-231
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linear operators preserving maximal column ranks of nonbinary boolean matrices
Autorzy:
Song, Seok-Zun
Yang, Sung-Dae
Hong, Sung-Min
Jun, Young-Bae
Kim, Seon-Jeong
Powiązania:
https://bibliotekanauki.pl/articles/728798.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Boolean matrix
semiring
linear operator on matrices
congruence operator on matrices
maximal column rank of a matrix
Boolean rank of a matrix
Opis:
The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 255-265
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modyfications of Csákánys Theorem
Autorzy:
Chajda, Ivan
Powiązania:
https://bibliotekanauki.pl/articles/728864.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
congruence class
idempotent element
permutable variety
Mal'cev condition
Opis:
Varieties whose algebras have no idempotent element were characterized by B. Csákány by the property that no proper subalgebra of an algebra of such a variety is a congruence class. We simplify this result for permutable varieties and we give a local version of the theorem for varieties with nullary operations.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 37-41
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Ring-like operations is pseudocomplemented semilattices
Autorzy:
Chajda, Ivan
Länger, Helmut
Powiązania:
https://bibliotekanauki.pl/articles/728882.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
pseudocomplemented semilattice
Boolean algebra
Boolean ring
distributivity
linear equation
ideal
congruence kernel
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 87-95
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Balanced congruences
Autorzy:
Chajda, Ivan
Eigenthaler, Günther
Powiązania:
https://bibliotekanauki.pl/articles/728742.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
balanced congruence
balanced algebra
balanced variety
Mal'cev condition
Opis:
Let V be a variety with two distinct nullary operations 0 and 1. An algebra ∈ V is called balanced if for each Φ,Ψ ∈ Con(), we have [0]Φ = [0]Ψ if and only if [1]Φ = [1]Ψ. The variety V is called balanced if every ∈ V is balanced. In this paper, balanced varieties are characterized by a Mal'cev condition (Theorem 3). Furthermore, some special results are given for varieties of bounded lattices.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 1; 105-114
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Congruence classes in Brouwerian semilattices
Autorzy:
Chajda, Ivan
Länger, Helmut
Powiązania:
https://bibliotekanauki.pl/articles/729047.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
congruence class
Brouwerian semilattice
ideal
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 229-237
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Maximal column rank preservers of fuzzy matrices
Autorzy:
Song, Seok-Zun
Park, Soo-Roh
Powiązania:
https://bibliotekanauki.pl/articles/728725.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
linear operator on matrices
fuzzy matrix
maximal column rank of a matrix
congruence operator on matrices
chain semiring
Opis:
This paper concerns two notions of rank of fuzzy matrices: maximal column rank and column rank. We investigate the difference of them. We also characterize the linear operators which preserve the maximal column rank of fuzzy matrices. That is, a linear operator T preserves maximal column rank if and only if it has the form T(X) = UXV with some invertible fuzzy matrices U and V.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 207-218
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Minimal formations of universal algebras
Autorzy:
Guo, Wenbin
Shum, K.
Powiązania:
https://bibliotekanauki.pl/articles/728734.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
universal algebra
congruence
formation
minimal subformation
Opis:
A class ℱ of universal algebras is called a formation if the following conditions are satisfied: 1) Any homomorphic image of A ∈ ℱ is in ℱ; 2) If α₁, α₂ are congruences on A and $A/α_{i} ∈ ℱ$, i = 1,2, then A/(α₁∩α₂) ∈ ℱ. We prove that any formation generated by a simple algebra with permutable congruences is minimal, and hence any formation containing a simple algebra, with permutable congruences, contains a minimum subformation. This result gives a partial answer to an open problem of Shemetkov and Skiba on formations of finite universal algebras proposed in 1989.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 201-205
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some modifications of congruence permutability and dually congruence regular varietie
Autorzy:
Chajda, Ivan
Eigenthaler, Günther
Powiązania:
https://bibliotekanauki.pl/articles/728754.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
congruence regularity
local congruence regularity
dual congruence regularity
local n-permutability
Opis:
It is well known that every congruence regular variety is n-permutable (in the sense of [9]) for some n ≥ 2. For the explicit proof see e.g. [2]. The connections between this n and Mal'cev type characterizations of congruence regularity were studied by G.D. Barbour and J.G. Raftery [1]. The concept of local congruence regularity was introduced in [3]. A common generalization of congruence regularity and local congruence regularity was given in [6] under the name "dual congruence regularity with respect to a unary term g". The natural problem arises what modification of n-permutability is satisfied by dually congruence regular varieties. The aim of this paper is to find out such a modification, to characterize varieties satisfying it by a Mal'cev type condition and to show connections with normally presented varieties (see e.g. [5], [8], [11]). The latter concept was introduced already by J. P≥onka under a different term; the names "normal identity" and "normal variety" were firstly used by E. Graczyńska in [8].
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 165-174
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some properties of congurence relations on orthomodular lattices
Autorzy:
Dorfer, Gerhard
Powiązania:
https://bibliotekanauki.pl/articles/728766.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
orthomodular lattice
congruence relation
congruence-regular
congruence-uniform
congruence-permutable
Opis:
In this paper congruences on orthomodular lattices are studied with particular regard to analogies in Boolean algebras. For this reason the lattice of p-ideals (corresponding to the congruence lattice) and the interplay between congruence classes is investigated. From the results adduced there, congruence regularity, uniformity and permutability for orthomodular lattices can be derived easily.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 1; 57-66
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The semantical hyperunification problem
Autorzy:
Denecke, Klaus
Koppitz, Jörg
Wismath, Shelly
Powiązania:
https://bibliotekanauki.pl/articles/728730.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypersubstitution
fully invariant congruence relation
hyperunification problem
Opis:
A hypersubstitution of a fixed type τ maps n-ary operation symbols of the type to n-ary terms of the type. Such a mapping induces a unique mapping defined on the set of all terms of type t. The kernel of this induced mapping is called the kernel of the hypersubstitution, and it is a fully invariant congruence relation on the (absolutely free) term algebra $F_{τ}(X)$ of the considered type ([2]). If V is a variety of type τ, we consider the composition of the natural homomorphism with the mapping induced by a hypersubstitution. The kernel of this mapping is called the semantical kernel of the hypersubstitution with respect to the given variety. If the pair (s,t) of terms belongs to the semantical kernel of a hypersubstitution, then this hypersubstitution equalizes s and t with respect to the variety. Generalizing the concept of a unifier, we define a semantical hyperunifier for a pair of terms with respect to a variety. The problem of finding a semantical hyperunifier with respect to a given variety for any two terms is then called the semantical hyperunification problem.
We prove that the semantical kernel of a hypersubstitution is a fully invariant congruence relation on the absolutely free algebra of the given type. Using this kernel, we define three relations between sets of hypersubstitutions and sets of varieties and introduce the Galois correspondences induced by these relations. Then we apply these general concepts to varieties of semigroups.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 175-200
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Balanced d-lattices are complemented
Autorzy:
Goldstern, Martin
Ploščica, Miroslav
Powiązania:
https://bibliotekanauki.pl/articles/729051.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
balanced congruence
balanced lattice
d-lattice
prime ideal
maximal ideal
Opis:
We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 1; 33-37
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Congruence submodularity
Autorzy:
Chajda, Ivan
Halaš, Radomír
Powiązania:
https://bibliotekanauki.pl/articles/728993.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
congruence lattice
modularity
congruence k-submodularity
Opis:
We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 2; 131-139
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 52

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