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Representing free Boolean algebras

Alan Dow, P. Nyikos (1992)

Fundamenta Mathematicae

Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with ℵ 1 generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not a subalgebra...

Ring-like operations is pseudocomplemented semilattices

Ivan Chajda, Helmut Länger (2000)

Discussiones Mathematicae - General Algebra and Applications

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 with unique symmetric difference related to quantum logic

Dietmar Dorninger, Helmut Länger, Maciej Maczyński (2001)

Discussiones Mathematicae - General Algebra and Applications

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.

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