We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.

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,...

We describe the isolation and characterization of Aberrant X segregation (Axs), a dominant female-specific meiotic mutation. Although Axs has little or no effect on the frequency or distribution of exchange, or on the disjunction of exchange bivalents, nonexchange X chromosomes undergo nondisjunction at high frequencies in Axs/+ and Axs/Axs females. This increased X chromosome nondisjunction is...

After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.

The book here reviewed consists of several articles written by different authors. We provide below short characteristics of each of the articles in the book. 1. Efficient distributed computation modulo a shared secret (Dario Catalano) The article concerns the subject of distributed computation. This is realized by the secret sharing protocols. The author presents several kinds of such protocols...

By a lattice we shall always mean a distributive lattice which is bounded, i.e. has both a bottom element 0 and a top element 1. Lattice homomorphisms will always be assumed to preserve 0 and 1. By a modality on a (distributive) lattice L = (L, ∧, ∨, ≤, 0, 1) is meant a map : L → L satisfying (1) 1 = 1, (2) (x ∧ y) = x ∧ y for x, y ∈ L. The pair (L, ) will be called a modalized (distributive) l...

This paper describes relations between a trilattice and corresponding meet-distributive lattices. The three meet-distributive lattices illustrate the five information levels, five logical levels and five levels of constructivity respectively. While the trilattice shows connections among the sexteen truth values in general, the three meetdistributive lattices visualize specific information about...

This paper proposes to study the lattice properties of two closed binary operations in the set of discrete fuzzy numbers. Using these operations to represent the meet and the join, we prove that the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers is a distributive lattice. Finally, we demonstrate that the subsets of discrete fuzzy numbers, which have the same...

It is well known that the only simple distributive lattice is the twoelement chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences. In this paper we show the existence of infinite complete-simple distributive lattices. “COMPLETE-SIMPLE” DISTRIBUTIVE LATTICES G. GRÄTZER A...

Distributive justice concerns the fair, just or equitable distribution of benefits and burdens. These benefits and burdens span all dimensions of social life and assume all forms, including income, economic wealth, political power, taxation, work obligations, education, shelter, health care, military service, community involvement and religious activities. Thus, justice arguments are often invo...