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Hyper-operations in effect algebras

Foundations
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Abstract

The structure of effect algebras is studied from the perspective of hyper-operations. It is shown that Riesz congruences are compatible with the hyper-meet operation and the hyper-join operation in effect algebras with the maximality property. Moreover, we prove that the quotient of an effect algebra E with the maximality property by a Riesz ideal \(I\ne E\) has the maximality property.

Keywords

Effect algebra Maximality property Hyper-operation Riesz congruence 

Notes

Acknowledgements

The author is highly grateful to the editor and the anonymous referees for their valuable comments and suggestions.

Funding

This study was funded by National Natural Science Foundation of China (Grant No. 11401128) and Doctoral Starting up Foundation of Guilin University of Technology.

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of ScienceGuilin University of TechnologyGuilinChina

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