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Wyświetlanie 1-3 z 3
Tytuł:
On the characterisation of Maltsev and Jónsson-Tarski algebras
Autorzy:
Smith, Jonathan
Powiązania:
https://bibliotekanauki.pl/articles/728924.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Mal'tsev variety
Mal'tsev algebra
Jónsson-Tarski variety
Jónsson-Tarski algebra
Goldie variety
Goldie algebra
congruence permutability
simplicial object
Opis:
There are very strong parallels between the properties of Mal'tsev and Jónsson-Tarski algebras, for example in the good behaviour of centrality and in the factorization of direct products. Moreover, the two classes between them include the majority of algebras that actually arise 'in nature'. As a contribution to the research programme building a unified theory capable of covering the two classes, along with other instances of good centrality and factorization, the paper presents a common framework for the characterisation of Mal'tsev and Jónsson-Tarski algebras. Mal'tsev algebras are characterized by simplicial identities in the product complex of an algebra. In the dual of a pointed variety, a simplicial object known as the pointed complex is then constructed. The basic simplicial Mal'tsev identity in the pointed complex characterises Jónsson-Tarski algebras. Higher-dimensional simplicial Mal'tsev identities in the pointed complex are characteristic of a class of algebras lying properly between Goldie and Jónsson-Tarski algebras.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 149-161
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:
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
    Wyświetlanie 1-3 z 3

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