A remark to the paper of M. Froda-Schechter: Préordres et équivalences dans l'ensemble des familles d'un ensemble
A representation of bounded commutative BCK-algebras.
A representation of orthomodular lattices
A representation of relatively complemented distributive lattices
A representation theorem for CAC lattices.
A representation theorem for certain Boolean lattices.
Let R be an associative ring with 1 and R-tors the somplete Brouwerian lattice of all hereditary torsion theories on the category of left R-modules. A well known result asserts that R is a left semiartinian ring iff R-tors is a complete atomic Boolean lattice. In this note we prove that if L is a complete atomic Boolean lattice then there exists a left semiartinian ring R such that L is lattice-isomorphic to R-tors.
A representation theorem for linearly ordered cardinal algebras
A representation theorem for tense -valued Łukasiewicz-Moisil algebras
In 2000, Figallo and Sanza introduced -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLM of tense -valued Łukasiewicz-Moisil algebras (or tense LM-algebras), namely -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras...
A result forO2-convergence to be topological in posets
In this paper, the α waybelow relation, which is determined by O2-convergence, is characterized by the order on a poset, and a sufficient and necessary condition for O2-convergence to be topological is obtained.
A rigid Boolean algebra that admits the elimination of Q21
Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier .
A sandwich theorem for monotone additive functions.
A scheme for congruence semidistributivity
A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.
A selection property of the boolean -calculus and some of its applications
A selection theorem for Boolean correspondences.
A set-theoretical equivalent of the prime ideal theorem for Boolean algebras
A sharp bound for the reconstruction of partitions.
A short note on lattices allowing disjunctive reasoning.
This short note shows that the scheme of disjunctive reasoning, a or b, not b : a, does not hold neither in proper ortholattices nor in proper de Morgan algebras. In both cases the scheme, once translated into the inequality b' · (a+b) ≤ a, forces the structure to be a boolean algebra.
A short note on separable frames
Following the introduction of separability in frames ([2]) we investigate further properties of this notion and establish some consequences of the Urysohn metrization theorem for frames that are frame counterparts of corresponding results in spaces. In particular we also show that regular subframes of compact metrizable frames are metrizable.
A shrinking of a category of societies is a universal partly ordered class
A simple basis of ideal terms of Brouwerian semilattices