Blocks of homogeneous effect algebras

@article{Jenvca2001BlocksOH,
  title={Blocks of homogeneous effect algebras},
  author={Gejza Jenvca},
  journal={Bulletin of the Australian Mathematical Society},
  year={2001},
  volume={64},
  pages={81 - 98}
}
  • Gejza Jenvca
  • Published 1 August 2001
  • Mathematics
  • Bulletin of the Australian Mathematical Society
Effect algebras, introduced by Foulis and Bennett in 1994, are partial algebras which generalise some well known classes of algebraic structures (for example orthomodular lattices, MV algebras, orthoalgebras et cetera). In the present paper, we introduce a new class of effect algebras, called homogeneous effect algebras. This class includes orthoalgebras, lattice ordered effect algebras and effect algebras satisfying the Riesz decomposition property. We prove that every homogeneous effect… 
Sharp and Meager Elements in Orthocomplete Homogeneous Effect Algebras
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It is proved that a complete lattice ordered effect algebra E is completely determined by the complete orthomodular lattice S(E), the BCK-algebra M(E) of meager elements and a mapping h:H(a) = [0,a] ∩ M(E).
Generalized homogeneous, prelattice and MV-effect algebras
TLDR
A necessary and sufficient condition is shown, when lattice operations of a such generalized effect algebra P are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra.
The three types of normal sequential effect algebras
TLDR
It is found that associativity forces normal SEAs satisfying the new axiom to be commutative, shedding light on the question of why the sequential product in quantum theory should be non-associative.
Hyper-operations in effect algebras
  • Wei Ji
  • Mathematics
    Soft Comput.
  • 2019
TLDR
It is shown that Riesz congruences are compatible with thehyper-meet operation and the hyper-join operation in effect algebras with the maximality property and it is proved that the quotient of an effect algebra E with the Maximality property by a RiesZ ideal has the maximalities property.
The block structure of complete lattice ordered effect algebras
  • Gejza Jenča
  • Mathematics
    Journal of the Australian Mathematical Society
  • 2007
Abstract 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
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We know that each effect algebra E is isomorphic to π(X) for some E-test spaces (X,T).We describe when π(x)∨π(y) and π(x) ∧ π(y) exists for x, y ∈ E(X,T). Moreover we give the formula for π(x) ∨ π(x)
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TLDR
It is proved that if there is a faithful state on the effect algebra, then any two standard observables that are smearings of the same (sharp) observable admit a generalized joint observable.
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On the set of bounded observables on an effect algebra, the Olson order defined by spectral resolutions and the standard order defined by a system of σ-additive states are introduced. We show that
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