A Hölder-type inequality for positive functionals on -algebras.
A hypervaluation of a ring onto a totally ordered non-cancellative semigroup without zero divisors.
A lattice of homomorphs
A Link Between Ordered Sets And Trees On The Rectangle Tree Hypothesis
A Loomis-Sikorski theorem for logics
A maximal chain approach to topology and order.
A Measure for Semialgebraic Sets Related to Boolean Complexity.
A measure-theoretic characterization of Boolean algebras among orthomodular lattices
We investigate subadditive measures on orthomodular lattices. We show as the main result that an orthomodular lattice has to be distributive (=Boolean) if it possesses a unital set of subadditive probability measures. This result may find an application in the foundation of quantum theories, mathematical logic, or elsewhere.
A metric on a system of ordered sets
In [3] a metric on a system of isomorphism classes of ordered sets was defined. In this paper we define another metric on the same system and investigate some of its properties. Our approach is motivated by a problem from practice.
A metrizable completely regular ordered space
We construct a completely regular ordered space such that is an -space, the topology of is metrizable and the bitopological space is pairwise regular, but not pairwise completely regular. (Here denotes the upper topology and the lower topology of .)
A Mixid Theory of Information - IV: Inset-Inaccuracy and Directed Divergence.
A new approach to representation of observables on fuzzy quantum posets
We give a representation of an observable on a fuzzy quantum poset of type II by a pointwise defined real-valued function. This method is inspired by that of Kolesárová [6] and Mesiar [7], and our results extend representations given by the author and Dvurečenskij [4]. Moreover, we show that in this model, the converse representation fails, in general.
A new characterization of orthomodular partially ordered sets
A new look at pointfree metrization theorems
We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context.
A new order relation for JB-algebras
A new view of relationship between atomic posets and complete (algebraic) lattices
In the context of the atomic poset, we propose several new methods of constructing the complete lattice and the algebraic lattice, and the mutual decision of relationship between atomic posets and complete lattices (algebraic lattices) is studied.
A non commutative generalization of -autonomous lattices
Pseudo -autonomous lattices are non-commutative generalizations of -autonomous lattices. It is proved that the class of pseudo -autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo -autonomous lattices can be described as their normal ideals.
A non-associative generalization of MV-algebras
A non-commutative generalization of -algebras
A normal form for some semigroups generated by idempotents