Josef Niederle

Boolean and distributive ordered sets: Characterization and representation by sets

Boolean ordered sets generalize Boolean lattices, and distributive ordered sets generalize distributive lattices. Ideals, prime ideals, and maximal ideals in ordered sets are defined, and some well-known theorems on Boolean lattices, such as the Glivenko-Stone theorem and the Stone representation theorem, are generalized to Boolean ordered sets. A prime ideal theorem for distributive ordered sets is formulated, and the Birkhoff representation theorem is generalized to distributive ordered sets. Fundamental are the embedding theorems for Boolean ordered sets and for distributive ordered sets.

On minimal residuated bounded mappings in atomistic lattices

Relationship between automorphisms and residuated bounded mappings in atomistic lattices is studied.

Homogeneous orthocomplete effect algebras are covered by MV-algebras

The aim of our paper is twofold. First, we thoroughly study the sets of meager and hypermeager elements. Second, we study a common generalization of orthocomplete and lattice effect algebras. We show that every block of an Archimedean homogeneous effect algebra satisfying this generalization is lattice ordered. Hence such effect algebras can be covered by ranges of observables. As a corollary, this yields that every block of a homogeneous orthocomplete effect algebra is lattice ordered. Therefore finite homogeneous effect algebras are covered by MV-algebras.

More about sharp and meager elements in Archimedean atomic lattice effect algebras

The aim of our paper is twofold. First, we thoroughly study the set of meager elements

Identities in Ordered Sets

\hbox{M}(E),

Triple Representation Theorem for Homogeneous Effect Algebras

the center

STRENGTHENED FIXED POINT PROPERTY AND PRODUCTS IN ORDERED SETS

\hbox{C}(E)