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 concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

We introduce “π-versions” of five familiar conditions for distributivity by applying the various conditions to 3-element antichains only. We prove that they are inequivalent concepts, and characterize them via exclusion systems. A lattice L satisfies D0π if a∧(b∨c) 6 (a∧b)∨c for all 3-element antichains {a, b, c}. We consider a congruence relation ∼ whose blocks are the maximal autonomous chain...

This article shows that the distributive laws of Beck in the bicategory of sets and matrices wherein monads are categories determine strict factorization systems on their composite monads Conversely it is shown that strict factorization systems on categories give rise to distributive laws Moreover these processes are shown to be mutually inverse in a precise sense Strict factorization systems a...

In this note we introduce and study algebras ( L , V, A, 1, 0,l) of type (2,2,1,1,1) such that ( L , V, A, 0 , l ) is a bounded distributive lattice and -,is an operator that satisfies the conditions -,(a V b ) = -,a A -,b and -0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras o...

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...

current research examines the impact of perceived justice (including distributive justice, procedural justice and interactional justice) on perceived service quality and customer behavioral intentions (including word of mouth, trust and revisit intention).statistical sample comprises 120 customers of iran insurance company in shiraz holding automobile insurance and have record of visiting the c...

Let L denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set (La,⊆) is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in (La,⊆) has a finite or infinite family of minimal forbidden subgraphs.

In 1990, we published the following result: Let m be a regular cardinal > א0. Every m-algebraic lattice L can be represented as the lattice of m-complete congruence relations of an m-complete modular lattice K. In this note, we present a short proof of this theorem. In fact, we present a significant improvement: The lattice K we construct is 2-distributive.

Let B be a complete Boolean algebra. We show that if λ is an infinite cardinal and B is weakly (λ, ω)-distributive, then B is (λ, 2)-distributive. Using a similar argument, we show that if κ is a weakly compact cardinal such that B is weakly (2, κ)distributive and B is (α, 2)-distributive for each α < κ, then B is (κ, 2)-distributive.