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Effect algebras and ring-like structures

Enrico G. BeltramettiMaciej J. Maczyński — 2003

Discussiones Mathematicae - General Algebra and Applications

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 algebra,...

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