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On Jauch-Piron effect algebras
by
Zdenka Riečanová
Department of Mathematics, Faculty of Electrical Engineering and Information Technology STU, Ilkovičova 3, SK-81219 Bratislava, Slovak Republic
Lattice and Order Theory
Recently there appeared new algebraic structures weakening the axiomatic systems of orthomodular lattices and MV-algebras. Especially those are effect algebras (introduced by D. Foulis and M.K. Bennett, 1994). Effect algebras may be carriers of states and probabilities in quantum or fuzzy probability theory. On the other hand there are even finite effect algebras admitting no states and probabilities. We show some families of effect algebras admitting sigma-additive or subadditive states (probabilities), even with the Jauch-Piron property. We show sufficient and necessary conditions for atomic lattice effect algebras to be unital and Jauch-Piron.
Date received: April 12, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # capw-44.