# 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…

## 18 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.

### Homogeneous orthocomplete effect algebras are covered by MV-algebras

- MathematicsFuzzy Sets Syst.
- 2013

### Triple Representation Theorem for Homogeneous Effect Algebras

- Mathematics2012 IEEE 42nd International Symposium on Multiple-Valued Logic
- 2012

The aim of our paper is to prove the Triple Representation Theorem, which was established by Jenca in the setting of complete lattice effect algebras, for a special class of homogeneous effect…

### 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.

### Triple Representation Theorem for orthocomplete homogeneous effect algebras

- Mathematics
- 2012

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…

### 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…

### Representable Effect Algebras and Observables

- Mathematics
- 2013

We introduce a class of monotone σ-complete effect algebras, called representable, which are σ-homomorphic images of a class of monotone σcomplete effect algebras of functions taking values in the…

### 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)…

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