A complete lattice L is constructively completely distributive CCD when the sup arrow from down closed subobjects of L to L has a left adjoint The Karoubian envelope of the bicategory of relations is biequivalent to the bicategory of CCD lattices and sup preserving arrows There is a restriction to order ideals and totally algebraic lattices Both biequivalences have left exact ver sions As appli...

Let L be a distributive lattice and G the abelian group with the following presentation. The generators of G are the elements of the lattice L, and the relations are (a V b) + (a A 6) = a + b where a and b are arbitrary elements of L, It is shown that G is free abelian. In particular, G is torsion free. The latter statement answers affirmatively a question posed several years ago by E. Weinberg...

A lattice L is spatial if every element of L is a join of completely join-irreducible elements of L (points), and strongly spatial if it is spatial and the minimal coverings of completely join-irreducible elements are well-behaved. Herrmann, Pickering, and Roddy proved in 1994 that every modular lattice can be embedded, within its variety, into an algebraic and spatial lattice. We extend this r...

In the early forties, R. P. Dilworth proved his famous result: Every finite distributive lattice D can be represented as the congruence lattice of a finite lattice L. In one of our early papers, we presented the first published proof of this result; in fact we proved: Every finite distributive lattice D can be represented as the congruence lattice of a finite sectionally complemented lattice L....

Let L be a finite distributive lattice. Let Sub0(L) be the lattice {S | S is a sublattice of L} ∪ {∅} and let ∗[Sub0(L)] be the length of the shortest maximal chain in Sub0(L). It is proved that if K and L are non-trivial finite distributive lattices, then ∗[Sub0(K × L)] = ∗[Sub0(K)] + ∗[Sub0(L)]. A conjecture from the 1984 Banff Conference on Graphs and Order is thus proved. 1 Motivation Let L...

S OF PAPERS SUBMITTED FOR PRESENTATION TO THE SOCIETY The following papers have been submitted to the Secretary and the Associate Secretaries of the Society for presentation at meetings of the Society. They are numbered serially throughout this volume. Cross references to them in the reports of the meetings will give the number of this volume, the number of this issue, and the serial number of ...

Qualitative calculi play a central role in representing and reasoning about qualitative spatial and temporal knowledge. This paper studies distributive subalgebras of qualitative calculi, which are subalgebras in which (weak) composition distributives over nonempty intersections. It has been proven for RCC5 and RCC8 that path consistent constraint network over a distributive subalgebra is alway...

Algebraic structures like fuzzy sub rings of L-Fuzzy sets have been well studied in the case where lattice L is distributive. In this paper axioms concepts can be generalised to not The aim current define concept L-fuzzy meet semi almost ideals and also Intutionistic . Investigate some theorems examples.

A finite distributive latticeD can be representedas the congruence lattice, ConL, of a finite lattice L. We shall discuss the combinatorial aspects of such—and related—representations, specifically, optimal size, breadth, and degree of symmetry.

The aim of the present paper is to define the localization BL-algebra of a BL-algebra A with respect to a topology F on A. In the last part of the paper is proved that the maximal BL-algebra of quotients (defined in [5]) and the BLalgebra of fractions relative to a ∧-closed system (defined in [4]) are BL-algebras of localization. A remarkable construction in ring theory is the localization ring...