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Triple Representation Theorem for orthocomplete homogeneous effect algebras

Abstract

The aim of our paper is twofold. First, we thoroughly study the set of meager elements M(E), the set of sharp elements S(E), and the center C(E) in the setting of meager-orthocomplete homogeneous effect algebras E. Second, we prove the Triple Representation Theorem for sharply dominating meager-orthocomplete homogeneous effect algebras, in particular orthocomplete homogeneous effect algebras.

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Correspondence to Jan Paseka.

Additional information

Presented by S. Pulmannova.

The second author gratefully acknowledges financial support of the Ministry of Education of the Czech Republic under the project MSM0021622409 and of Masaryk University under the grant 0964/2009. Both authors acknowledge the support by ESF Project CZ.1.07/2.3.00/20.0051 Algebraic methods in Quantum Logic of the Masaryk University.

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Niederle, J., Paseka, J. Triple Representation Theorem for orthocomplete homogeneous effect algebras. Algebra Univers. 68, 197–220 (2012). https://doi.org/10.1007/s00012-012-0205-0

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  • DOI: https://doi.org/10.1007/s00012-012-0205-0

2010 Mathematics Subject Classification

  • Primary: 03G12
  • Secondary: 06D35
  • 06F25
  • 81P10

Key words and phrases

  • homogeneous effect algebra
  • orthocomplete effect algebra
  • meager-orthocomplete effect algebra
  • lattice effect algebra
  • center
  • atom
  • sharp element
  • meager element
  • hypermeager element