Congruence Lattices of Finite Lattices as Concept Lattices

1990 ◽  
pp. 323-325
Author(s):  
Sigrid Knecht ◽  
Rudolf Wille
Keyword(s):  
Concept Lattices ◽  
Finite Lattices ◽  
Congruence Lattices

scholarly journals CONGRUENCE FD-MAXIMAL VARIETIES OF ALGEBRAS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250053 ◽  
Author(s):  
PIERRE GILLIBERT ◽  
MIROSLAV PLOŠČICA
Keyword(s):  
Necessary Condition ◽  
Finitely Generated ◽  
Distributive Variety ◽  
Finite Lattices ◽  
Congruence Lattices ◽  
Congruence Distributive Variety ◽  
Congruence Distributive ◽  
Special Congruence

We study the class of finite lattices that are isomorphic to the congruence lattices of algebras from a given finitely generated congruence-distributive variety. If this class is as large as allowed by an obvious necessary condition, the variety is called congruence FD-maximal. The main results of this paper characterize some special congruence FD-maximal varieties.

scholarly journals Congruence Representations of Join-homomorphisms of Finite Distributive Lattices: Size and Breadth

2000 ◽  
Vol 68 (1) ◽  
pp. 85-103 ◽  
Author(s):  
G. Grätzer ◽  
H. Lakser ◽  
E. T. Schmidt
Keyword(s):  
Distributive Lattices ◽  
Irreducible Elements ◽  
Finite Lattices ◽  
Congruence Lattices ◽  
Finite Distributive Lattices

AbstractLet K and L be lattices, and let ϕ be a homomorphism of K into L.Then ϕ induces a natural 0-preserving join-homomorphism of Con K into Con L.Extending a result of Huhn, the authors proved that if D and E are finite distributive lattices and ψ is a 0-preserving join-homomorphism from D into E, then D and E can be represented as the congruence lattices of the finite lattices K and L, respectively, such that ψ is the natural 0-preserving join-homomorphism induced by a suitable homomorphism ϕ: K → L. Let m and n denote the number of join-irreducible elements of D and E, respectively, and let k = max (m, n). The lattice L constructed was of size O(22(n+m)) and of breadth n+m.We prove that K and L can be constructed as ‘small’ lattices of size O(k5) and of breadth three.

scholarly journals Recent results in partition (Ramsey) theory for finite lattices

1981 ◽  
Vol 35 (1-3) ◽  
pp. 185-198 ◽  
Author(s):  
Hans Jürgen Prömel ◽  
Bernd Voigt
Keyword(s):  
Ramsey Theory ◽  
Finite Lattices

scholarly journals Gradation of Fuzzy Preconcept Lattices

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 41
Author(s):  
Alexander Šostak ◽  
Ingrīda Uļjane ◽  
Māris Krastiņš
Keyword(s):  
Fuzzy Information ◽  
Concept Lattices ◽  
Practical Applications ◽  
Fuzzy Concept ◽  
The One ◽  
Practical Nature

Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information then the one based on fuzzy concept lattices. We consider two possible gradation methods of fuzzy preconcept lattice—an inner one, called D-gradation and an outer one, called M-gradation, study their properties, and illustrate by a series of examples, in particular, of practical nature.

scholarly journals Congruence pairs of principal MS-algebras and perfect extensions

2020 ◽  
Vol 70 (6) ◽  
pp. 1275-1288
Author(s):  
Abd El-Mohsen Badawy ◽  
Miroslav Haviar ◽  
Miroslav Ploščica
Keyword(s):  
Boolean Algebra ◽  
Congruence Lattices ◽  
Descriptive Solution ◽  
The One ◽  
Special Case ◽  
Congruence Pair

AbstractThe notion of a congruence pair for principal MS-algebras, simpler than the one given by Beazer for K2-algebras [6], is introduced. It is proved that the congruences of the principal MS-algebras L correspond to the MS-congruence pairs on simpler substructures L°° and D(L) of L that were associated to L in [4].An analogy of a well-known Grätzer’s problem [11: Problem 57] formulated for distributive p-algebras, which asks for a characterization of the congruence lattices in terms of the congruence pairs, is presented here for the principal MS-algebras (Problem 1). Unlike a recent solution to such a problem for the principal p-algebras in [2], it is demonstrated here on the class of principal MS-algebras, that a possible solution to the problem, though not very descriptive, can be simple and elegant.As a step to a more descriptive solution of Problem 1, a special case is then considered when a principal MS-algebra L is a perfect extension of its greatest Stone subalgebra LS. It is shown that this is exactly when de Morgan subalgebra L°° of L is a perfect extension of the Boolean algebra B(L). Two examples illustrating when this special case happens and when it does not are presented.

On context patterns associated with concept lattices

Order ◽  
1993 ◽  
Vol 10 (4) ◽  
pp. 363-373
Author(s):  
Winfried Geyer
Keyword(s):  
Concept Lattices
Sign in / Sign up

Export Citation Format

Share Document