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...

A nearlattice is a meet semilattice A in which every initial segment Ap := {x : x ≤ p} happens to be a join semilattice (hence, a lattice) with respect to the natural ordering of A. If all lattices Ap are distributive, the nearlattice itself is said to be distributive. It is known that a distributive nearlattice can be represented as a nearlattice of sets. We call an algebra (A,∧,∨) of type (2,...

A semimodular lattice L of finite length will be called an almost-geometric lattice, if the order J(L) of its nonzero join-irreducible elements is a cardinal sum of at most two-element chains. We prove that each finite distributive lattice is isomorphic to the lattice of congruences of a finite almost-geometric lattice.

In this work we generalize previous constructions of fuzzy set categories, introduced in [5], by considering L-fuzzy sets in which the values of the characteristic functions run on a completely distributive lattice, rather than in the unit real interval. Later, these L-fuzzy sets are used to define the L-fuzzy categories, which are proven to be rational. In the final part of the paper, the L-fu...

Let L be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct C(L), called the tower extension of C (indexed by L). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spac...

England Abstract A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the simplicial homology of the underlying simplicial complex in the case of a digraph algebra. These groups are computable and useful. In parti...

Abstract. A new form of α-compactness is introduced in L-topological spaces by α-open L-sets and their inequality where L is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice L. It can also be characterized by means of α-closed L-sets and their inequality. When L is a completely distributive de Morgan algebra, its many characterizations are presented and the re...

The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame $L$. A definition of (strongly) completelydistributive $L$-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $L$-ordereds...

Stone algebras have been characterized by Chen and Grätzer in terms of triples (B;D;'), whereD is a distributive lattice with 1; B is a Boolean algebra, and ' is a bounded lattice homomorphism from B into the lattice of …lters of D: If D is bounded, the construction of these characterizing triples is much simpler, since the homomorphism ' can be replaced by one from B into D itself. The triple ...

We prove that the skeleton of a product of finitely many finite distributive lattices is isomorphic to the product of skeletons of its factors. Thus, it is possible to construct finite distributive lattices with a given directly reducible skeleton by reducing the problem to the skeleton factors. Although not all possible lattices can be obtained this way, we show that it works for the smallest ...