# 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} }

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…

## 14 Citations

Sharp and Meager Elements in Orthocomplete Homogeneous Effect Algebras

- MathematicsOrder
- 2010

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

- Mathematics, Computer ScienceKybernetika
- 2005

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

- MathematicsQuantum
- 2020

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

- MathematicsSoft Comput.
- 2019

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

- MathematicsJournal 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…

Joins and meets in effect algebras

- Mathematics
- 2021

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)…

Compatibility of observables on effect algebras

- MathematicsSoft Comput.
- 2016

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.

Quantum Observables and Effect Algebras

- Mathematics
- 2016

We study observables on monotone σ-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. We characterize sharp observables of a…

On Orders of Observables on Effect Algebras

- Mathematics
- 2016

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…

Quantum Observables and Effect Algebras

- Mathematics
- 2016

We study observables on monotone σ-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. The set of sharp elements of a monotone…

## References

SHOWING 1-10 OF 29 REFERENCES

Phi-symmetric effect algebras

- Mathematics, Computer Science
- 1995

It is shown that every interval effect algebra with a lattice-ordered ambient group is Φ-symmetric, and its group is the one constructed by Ravindran in his proof that every effect algebra that has the Riesz decomposition property is an interval algebra.

Quotients of partial abelian monoids

- Mathematics
- 1997

Abstract. A hierarchy of partial abelian structures is considered. In an order of decreasing generality, these structures include partial abelian monoids (PAM), cancellative PAMs (CPAM), effect…

The center of an effect algebra

- Mathematics
- 1995

An effect algebra is a partial algebra modeled on the standard effect algebra of positive self-adjoint operators dominated by the identity on a Hilbert space. Every effect algebra is partially…

Algebraic analysis of many valued logics

- Mathematics
- 1958

This paper is an attempt at developing a theory of algebraic systems that would correspond in a natural fashion to the No-valued propositional calculus(2). For want of a better name, we shall call…

Effect algebras and unsharp quantum logics

- Mathematics
- 1994

The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among…

Filters and supports in orthoalgebras

- Mathematics
- 1992

An orthoalgebra, which is a natural generalization of an orthomodular lattice or poset, may be viewed as a “logic” or “proposition system” and, under a welldefined set of circumstances, its elements…

Orthomodular Lattices: Algebraic Approach

- Mathematics
- 1985

I: Introduction.- II: Elementary Theory of Orthomodular Lattices.- 1. Ortholattices.- 2. Commutativity.- 3. Orthomodular lattices.- 4. Properties of commutativity in orthomodular lattices.- 5.…

An Introduction to Hilbert Space and Quantum Logic

- Mathematics
- 1989

1. Experiments, Measure, and Integration.- A. Measures.- Experiments and weight functions, expected value of a weight function, measures, Lebesgue measure, signed measures, complex measures,…

Toward a formal language for unsharp properties

- Computer Science
- 1989

Some algebraic structures of the set of all effects are investigated and summarized in the notion of a(weak) orthoalgebra. It is shown that these structures can be embedded in a natural way in…

Operational Quantum Physics

- Physics
- 1997

Quantum physics is certainly one of the greatest scientific achievements of the 20th century. Nevertheless, there has always been a gap between the formalistics approach of quantum theory and its…