Displaying similar documents to “Effect algebras and ring-like structures”

Ring-like structures with unique symmetric difference related to quantum logic

Dietmar Dorninger, Helmut Länger, Maciej Maczyński (2001)

Discussiones Mathematicae - General Algebra and Applications

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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.

p -rings and ring-logics

Alfred L. Foster (1951)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Rings Which Can Be Recovered by Means of the Difference

Ivan Chajda, Filip Švrček (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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It is well known that to every Boolean ring ℛ can be assigned a Boolean algebra ℬ whose operations are term operations of ℛ . Then a symmetric difference of ℬ together with the meet operation recover the original ring operations of ℛ . The aim of this paper is to show for what a ring ℛ a similar construction is possible. Of course, we do not construct a Boolean algebra but only so-called lattice-like structure which was introduced and treated by the authors in a previous paper. In particular,...

Closure rings

Barry J. Gardner, Tim Stokes (1999)

Commentationes Mathematicae Universitatis Carolinae

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We consider rings equipped with a closure operation defined in terms of a collection of commuting idempotents, generalising the idea of a topological closure operation defined on a ring of sets. We establish the basic properties of such rings, consider examples and construction methods, and then concentrate on rings which have a closure operation defined in terms of their lattice of central idempotents.

Some distributivities in GBbi-QRs characterizing Boolean rings

Joanna Kaleta (2004)

Discussiones Mathematicae - General Algebra and Applications

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This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.