Riesz groups with a finite number of disjoint elements
Riesz spaces and the ultrafilter theorem, I
Riesz spaces of order bounded disjointness preserving operators
Let , be Archimedean Riesz spaces and be the ordered vector space of all order bounded operators from into . We define a Lamperti Riesz subspace of to be an ordered vector subspace of such that the elements of preserve disjointness and any pair of operators in has a supremum in that belongs to . It turns out that the lattice operations in any Lamperti Riesz subspace of are given pointwise, which leads to a generalization of the classic Radon-Nikod’ym theorem for Riesz homomorphisms....
Rigid Boolean Algebras
Rigid extensions of -groups of continuous functions
Let , and denote the -groups of integer-valued, rational-valued and real-valued continuous functions on a topological space , respectively. Characterizations are given for the extensions to be rigid, major, and dense.
Ring-like operations is pseudocomplemented semilattices
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
Ring-like structures corresponding to generalized orthomodular lattices
Ring-like structures derived from -lattices with antitone involutions
Using the concept of the -lattice introduced recently by V. Snášel we define -lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.
Ring-like structures with unique symmetric difference related to quantum logic
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
Rings and Partly Ordered Systems.
Rings in Post algebras.
Rings Satisfying a Not-Necessarily Transitive Relation.
Rotations of -lattices
In [2], J. Klimes studied rotations of lattices. The aim of the paper is to research rotations of the so-called -lattices introduced in [3] by V. Snasel.
Rough subalgebras of some binary algebras connected with logics.