A characterization of polarities whose lattice of polars is Boolean
A note on Möbius inversion over power set lattices
In this paper, we establish a theorem on Möbius inversion over power set lattices which strongly generalizes an early result of Whitney on graph colouring.
A note on the product of measure algebras
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.
Announcements of new results
Bemerkung zu der Arbeit: „Die Anwendung der Polarität auf die direkten Produktzerlegungen einer Gruppe‟ von František Šik
Boolean algebras with a unary operator
Boolean concept lattices and good contexts
Boolean games – Classifying strategies and omitting cardinality assumptions
Booloïdes
Canonical ordering theorems, a first attempt
Canonical partition theorems for finite distributive lattices
Cellularity of free products of Boolean algebras (or topologies)
The aim this paper is to present an answer to Problem 1 of Monk [10], [11]. We do this by proving in particular that if μ is a strong limit singular cardinal, and then there are Boolean algebras such that . Further we improve this result, deal with the method and the necessity of the assumptions. In particular we prove that if is a ccc Boolean algebra and then satisfies the λ-Knaster condition (using the “revised GCH theorem”).
Choice principles in Węglorz’ models
Węglorz' models are models for set theory without the axiom of choice. Each one is determined by an atomic Boolean algebra. Here the algebraic properties of the Boolean algebra are compared to the set theoretic properties of the model.
Connectivity properties of sequential Boolean algebras
Convergences and higher degrees of distributivity of lattice ordered groups and of Boolean algebras
Die Anwendung der Polarität auf die direkten Produktzerlegungen einer Gruppe
Die atomare Struktur topologischer Boolescher Ringe und s-beschränkter Inhalte
Die Operationen in der Klasse komplementärer Verbände
Disjoint sequences in Boolean algebras
We deal with the system of all sequential convergences on a Boolean algebra . We prove that if is a sequential convergence on which is generated by a set of disjoint sequences and if is any element of , then the join exists in the partially ordered set . Further we show that each interval of is a Brouwerian lattice.