We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large. As an application, we prove various results of which the following is a prototype: If every diagram, indexed by a lattice, of finite Boolean 〈∨, 0〉-semilattices with 〈∨, 0〉-embeddings, can be lifted with respect to the Conc functor on lattices, then so can every diagra...

This paper describes a method for computing the fundamental unit and regulator of a purely cubic congruence function field of unit rank 1. The technique is based on Voronoi’s algorithm for generating a chain of successive minima in a multiplicative cubic lattice which is used for calculating the fundamental unit and regulator of a purely cubic number field.

Imai and Iséki [1] introduced the concept of BCK-algebra as a generalization of notions of set difference operation and propositional calculus. The notion of pseudo-BCK algebra was introduced by Georgescu and Iorgulescu [2] as generalization of BCK-algebras not assuming commutativity. Hájek [3] introduced the concept of BL-algebras as the general semantics of basic fuzzy logic (BL-logic). Iorgu...

Our result implies that the natural representation of Sub V as a congruence lattice is the best one, i.e., uses the minimum number of operations. This result is easy to obtain—see § 1. In the remainder of the paper we find further necessary conditions for the representability of an algebraic lattice L with <Λ; operations. Necessary and sufficient conditions seem impossible at this stage of know...

The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras algebraize the rst-order predicate logic. In this paper we prove that the variety of lambda abstraction algebras is not congruence modular and that the lattice of lambda theories is not modular.

We analyze the problem of uniqueness characterization groups by their weak congruence lattices. discuss possibility that same algebraic lattice L acts as a group in more than one way, so corresponding diagonals are represented different elements L. If this is impossible, is, if can be interpreted single we say sharp lattice. prove many classes have In particular, connections among isomorphisms ...