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Wyświetlanie 1-15 z 26
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:
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:
Congruences on bands of π-groups
Autorzy:
Maity, Sunil
Powiązania:
https://bibliotekanauki.pl/articles/728928.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
group congruence
completely regular semigroup congruence
Opis:
A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. The present paper is devoted to the study of completely regular semigroup congruences on bands of π-groups.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2013, 33, 1; 5-11
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
Tytuł:
Filters of lattices with respect to a congruence
Autorzy:
Sambasiva Rao, M.
El-Mohsen Badawy, Abd
Powiązania:
https://bibliotekanauki.pl/articles/729197.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
congruence
filter
closure operator
θ-filter
congruence lattice
Opis:
Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of $L_{/θ}$ is obtained.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2014, 34, 2; 213-219
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the lattice of congruences on inverse semirings
Autorzy:
Bhuniya, Anwesha
Bhuniya, Anjan
Powiązania:
https://bibliotekanauki.pl/articles/728800.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
inverse semirings
trace
kernel
Clifford congruence
least Clifford congruence
Opis:
Let S be a semiring whose additive reduct (S,+) is an inverse semigroup. The relations θ and k, induced by tr and ker (resp.), are congruences on the lattice C(S) of all congruences on S. For ρ ∈ C(S), we have introduced four congruences $ρ_{min}, ρ_{max}, ρ^{min}$ and $ρ^{max}$ on S and showed that $ρθ = [ρ_{min},ρ_{max}]$ and $ρκ = [ρ^{min},ρ^{max}]$. Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if $ρ_{max}$ is a distributive lattice congruence and $ρ^{max}$ is a skew-ring congruence on S. If η (σ) is the least distributive lattice (resp. skew-ring) congruence on S then η ∩ σ is the least Clifford congruence on S.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2008, 28, 2; 193-208
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Congruences on semilattices with section antitone involutions
Autorzy:
Chajda, Ivan
Powiązania:
https://bibliotekanauki.pl/articles/729025.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
semilattice
section
antitone involution
congruence kernel
filter
congruence distributivity
3-permutability
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2010, 30, 2; 207-215
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:
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:
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:
Clifford congruences on generalized quasi-orthodox GV-semigroups
Autorzy:
Maity, Sunil
Powiązania:
https://bibliotekanauki.pl/articles/729073.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Clifford semigroup
Clifford congruence
generalized quasi-orthodox semigroup
Opis:
A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. A completely π-regular semigroup S is said to be a GV-semigroup if all the regular elements of S are completely regular. The present paper is devoted to the study of generalized quasi-orthodox GV-semigroups and least Clifford congruences on them.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2013, 33, 2; 137-145
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:
The Clifford semiring congruences on an additive regular semiring
Autorzy:
Bhuniya, A.
Powiązania:
https://bibliotekanauki.pl/articles/729215.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
additive regular semiring
skew-ring
trace
kernel
Clifford congruence
Opis:
A congruence ρ on a semiring S is called a (generalized)Clifford semiring congruence if S/ρ is a (generalized)Clifford semiring. Here we characterize the (generalized)Clifford congruences on a semiring whose additive reduct is a regular semigroup. Also we give an explicit description for the least (generalized)Clifford congruence on such semirings.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2014, 34, 2; 143-153
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On QI-algebras
Autorzy:
Bandaru, Ravi Kumar
Powiązania:
https://bibliotekanauki.pl/articles/38140990.pdf
Data publikacji:
2017-12-20
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
BI-algebra
QI-algebra
right distributive
ideal
congruence kernel
Opis:
In this paper, the notion of a QI-algebra is introduced which is a generalization of a BI-algebra and there are studied its properties. We considered ideals, congruence kernels in a QI-algebra and characterized congruence kernels whenever a QI-algebra is right distributive.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2017, 37, 2; 137-145
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
Wyświetlanie 1-15 z 26

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