-rings and ring-logics
Alfred L. Foster (1951)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Alfred L. Foster (1951)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Yaqub, Adil (1967)
Portugaliae mathematica
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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.
Putcha, Mohan S., Yaqub, Adil (1981)
Portugaliae mathematica
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Artemovych, O.D. (2004)
International Journal of Mathematics and Mathematical Sciences
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Yau, Donald (2004)
International Journal of Mathematics and Mathematical Sciences
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Enrico G. Beltrametti, Maciej J. Maczyński (2003)
Discussiones Mathematicae - General Algebra and Applications
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The dichotomic physical quantities, also called propositions, can be naturally associated to maps of the set of states into the real interval [0,1]. We show that the structure of effect algebra associated to such maps can be represented by quasiring structures, which are a generalization of Boolean rings, in such a way that the ring operation of addition can be non-associative and the ring multiplication non-distributive with respect to addition. By some natural assumption on the effect...