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The block structure of complete lattice ordered effect algebras

Part of: Algebraic logic Modular lattices, complemented lattices

Published online by Cambridge University Press:  09 April 2009

Gejza Jenča
Gejza Jenča
Affiliation:
Department of Mathematics Faculty of Electrical Engineering and Information TechnologyIlkovičova 3812 19 [email protected]
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Abstract

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We prove that every for every complete lattice-ordered effect algebra E there exists an orthomodular lattice O(E) and a surjective full morphism øE: O(E) → E which preserves blocks in both directions: the (pre)imageofa block is always a block. Moreover, there is a 0, 1-lattice embedding : E → O(E).

MSC classification

Secondary: 06C15: Complemented lattices, orthocomplemented lattices and posets 03G12: Quantum logic 81P10: Logical foundations of quantum mechanics; quantum logic
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 2 , October 2007 , pp. 181 - 216
Copyright
Copyright © Australian Mathematical Society 2007

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