Commutative semigroups whose lattice of tolerances is Boolean
Compatibility and central elements in pseudo-effect algebras
An equivalent definition of compatibility in pseudo-effect algebras is given, and its relationships with central elements are investigated. Furthermore, pseudo-MV-algebras are characterized among pseudo-effect algebras by means of compatibility.
Compatibility and partial compatibility in quantum logics
Compatibility in orthomodular posets
Compatibility problem in quasi-orthocomplemented posets
Complements in the lattice of all topologies of topological groups
Complements in the lattice of uniformities
Complete co-atomic lattices with enough primes.
Compressible groups
Congruence kernels of orthoimplication algebras.
Congruences and ideals in lattice effect algebras as basic algebras
Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.
Congruences and isotone maps on partially ordered sets.
Continuity and linear extensions of quantum measures on Jordan operator algebras.
Control and separating points of modular functions
Das Assoziativgesetz als Kummutativitätsaxiom in Boole'schen Zwerchverbänden.
Decomposition of -group-valued measures
We deal with decomposition theorems for modular measures defined on a D-lattice with values in a Dedekind complete -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition for -group-valued...
Descriptions of state spaces of orthomodular lattices (the hypergraph approach)
Using the general hypergraph technique developed in [7], we first give a much simpler proof of Shultz's theorem [10]: Each compact convex set is affinely homeomorphic to the state space of an orthomodular lattice. We also present partial solutions to open questions formulated in [10] - we show that not every compact convex set has to be a state space of a unital orthomodular lattice and that for unital orthomodular lattices the state space characterization can be obtained in the context of unital...
Die Operationen in der Klasse komplementärer Verbände
Distinguishing subsets in lattices
Distributivity in finitely generated orthomodular lattices