Finiteorthoatomistic effect algebras and regular algebraic E-test spaces
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Joanna Kaleta
und
Grzegorz BiĆczak
Abstract
In this article we consider two categories: the category of finiteorthoatomistic effect algebras and the category of regular algebraic E-test spaces. S. Gudder introduced (algebraic) E-test spaces and showed that for each algebraic E-test space (X; đŻ) there exists an effect algebra Î (X). Moreover Î is a covariant functor from the category of algebraic E-test spaces to the category of effect algebras. We show that the category of regular and algebraic E-test spaces is equivalent to the category of finiteorthoatomistic effect algebras. We proved that atoms in effect algebras corresponding to regular and algebraic E-test spaces are perspectivity classes of characteristic functions of one-element sets. We found an example of algebraic E-test space which is not regular and in corresponding E-test space some perspectivity class of the characteristic function of a singleton is not an atom.
(Communicated by Mirko Navara)
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Artikel in diesem Heft
- A new categorical equivalence for stone algebras
- On special classes of prime filters in BL-algebras
- A note on characterized and statistically characterized subgroups of đ = â/â€
- New Young-type integral inequalities using composition schemes
- The structure of pseudo-n-uninorms with continuous underlying functions
- Jensen-type inequalities for a second-order differential inequality condition
- A direct proof of the characterization of the convexity of the discrete Choquet integral
- Envelope of plurifinely plurisubharmonic functions and complex Monge-AmpĂšre type equation
- Fekete-Szegö inequalities for Ί-parametric and ÎČ-spirllike mappings of complex order in ân
- Entire function sharing two values partially with its derivative and a conjecture of Li and Yang
- Oscillatory properties of third-order semi-canonical dynamic equations on time scales via canonical transformation
- Weighted B-summability and positive linear operators
- Some properties and applications of convolution algebras
- On measures of Ï-noncompactess in F-spaces
- On the kolmogorovâfellerâgut weak law of large numbers for triangular arrays of rowwise and pairwise negatively dependent random variables
- Intermediately trimmed sums of oppenheim expansions: A strong law
- Novel weighted distribution: Properties, applications and web-tool
- On the q-Gamma distribution: Properties and inference
- Finiteorthoatomistic effect algebras and regular algebraic E-test spaces
- Prof. RNDr. Anatolij DvureÄenskij, DrSc. 75th anniversary
