We describe G-sets whose congruences satisfy some natural lattice or multiplicative restrictions. In particular, we determine G-sets with distributive, arguesian, modular, upper or lower semimodular congruence lattice as well as congruence n-permutable G-sets for n = 2, 2.5, 3.

It is proved that every (universal) algebra A with distributive and permutable structure lattice is isomorphic with the algebra of all global sections with compact supports of a sheaf of homomorphic images of A over a topological space. This completely generalises the corresponding result of Klaus Keimel for /-rings. Introduction. The following note is a preliminary report on the investigations...

We discuss the possible structures for and mutual relationships between a finite distributive lattice L, a maximal sublattice M of L and the corresponding ‘remainder’ R = L\M with the aid of Birkhoff duality, and contrast the results with the analogous situations for a general finite lattice L. @ 1999 Elsevier Science B.V. All rights reserved

We study some distributive lattices arising in the combinatorics of lattice paths. In particular, for the Dyck, Motzkin and Schröder lattices we describe the spectrum and we determine explicitly the Euler characteristic in terms of natural parameters of lattice paths. AMS Classification: Primary: 06D05; Secondary: 06A07.

We introduce the class of bounded distributive lattices with two operators, and ∇, the first between the lattice and the set of its ideals, and the second between the lattice and the set of its filters. The results presented can be understood as a generalization of the results obtained by S. Celani.

In this paper we present a method (linear in the size of the formal context) to solve the seriation problem for formal contexts. We show that any maximal solution can be represented by a PQ-Tree. Moreover, the set of PQ-Trees can be seen as a distributive lattice. This lattice yields a consensus method which deals with the multiple solutions.

A partial lattice P is ideal-projective, with respect to a class C of lattices, if for every K ∈ C and every homomorphism φ of partial lattices from P to the ideal lattice of K, there are arbitrarily large choice functions f : P → K for φ that are also homomorphisms of partial lattices. This extends the traditional concept of (sharp) transferability of a lattice with respect to C. We prove the ...

In the present paper, the intuitionistic fuzzy LI -ideal theory in lattice implication algebras is further studied. Some new properties and equivalent characterizations of intuitionistic fuzzy LI -ideals are given. Representation theorem of intuitionistic fuzzy LI -ideal which is generated by an intuitionistic fuzzy set is established. It is proved that the set consisting of all intuitionistic ...

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to ...