We maximize the total height of order ideals in direct products of finitely many finite chains. We also consider several order ideals simultaneously. As a corollary, a shifting property of some integer sequences, including digit sum sequences, is derived.
In this paper it is proved that the lattice of additive hereditary properties of finite graphs is completely distributive and that it does not satisfy the Jordan-Dedekind condition for infinite chains.
For an n-valued Łukasiewicz-Moisil algebra L (or LM n-algebra for short) we denote by F n(L) the lattice of all n-filters of L. The goal of this paper is to study the lattice F n(L) and to give new characterizations for the meet-irreducible and completely meet-irreducible elements on F n(L).
Through the study of frame congruences, new characterizations of the paracompactness of frames are obtained.
In this paper we investigate the relation between the lattice of varieties of pseudo -algebras and the lattice of varieties of lattice ordered groups.
Several open problems posed during FSTA 2006 (Liptovský Ján, Slovakia) are presented. These problems concern the classification of strict triangular norms, Lipschitz t-norms, interval semigroups, copulas, semicopulas and quasi- copulas, fuzzy implications, means, fuzzy relations, MV-algebras and effect algebras.
Closure -algebras are introduced as a commutative generalization of closure -algebras, which were studied as a natural generalization of topological Boolean algebras.