Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 003, 9 pages      arXiv:1001.1322      https://doi.org/10.3842/SIGMA.2010.003
Contribution to the Proceedings of the 5-th Microconference Analytic and Algebraic Methods V

Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

Jan Paseka
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlárská 2, CZ-611 37 Brno, Czech Republic

Received September 29, 2009, in final form January 07, 2010; Published online January 08, 2010

Abstract
Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)-continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.

Key words: effect algebra; state; modular lattice; finite element; compact element.

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