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.
KeywordsEffect algebra Maximality property Hyper-operation Riesz congruence
The author is highly grateful to the editor and the anonymous referees for their valuable comments and suggestions.
This study was funded by National Natural Science Foundation of China (Grant No. 11401128) and Doctoral Starting up Foundation of Guilin University of Technology.
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Conflict of interest
The author declares that he has no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.