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Hull mappings and dimension effect algebras

In: Mathematica Slovaca, vol. 61, no. 3
David Foulis - Sylvia Pulmannová
Detaily:
Rok, strany: 2011, 485 - 522
Kľúčové slová:
effect algebra, boolean algebra, hull mapping, monad, dyad, type-determining, Sherstnev-Kalinin congruence, dimension equivalence relation, dimension effect algebra, simple element, finite element, types I, II, and III
O článku:
An effect algebra (EA) is a partial algebraic structure, originally formulated as an algebraic base for unsharp quantum measurements. The class of EAs includes, as special cases, several partially ordered algebraic structures, including orthomodular lattices (OMLs) and orthomodular posets (OMPs), hitherto used as mathematical models for experimentally verifiable propositions pertaining to physical systems. Moreover, MV-algebras, which are mathematical models for many-valued logics, are special cases of EAs. The present paper studies generalizations to EAs of the hull mapping featured in L. Loomis's dimension theory for complete OMLs and develops a theory of direct decomposition for EAs with a hull mapping. A. Sherstnev and V. Kalinin have extended Loomis's dimension theory to orthocomplete OMPs, and here it is further extended to orthocomplete EAs; moreover, a corresponding direct decomposition into types I, II, and III is obtained using the hull mapping induced by the dimension equivalence relation.
Ako citovať:
ISO 690:
Foulis, D., Pulmannová, S. 2011. Hull mappings and dimension effect algebras. In Mathematica Slovaca, vol. 61, no.3, pp. 485-522. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0025-2

APA:
Foulis, D., Pulmannová, S. (2011). Hull mappings and dimension effect algebras. Mathematica Slovaca, 61(3), 485-522. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0025-2
O vydaní: