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.
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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.
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Communicated by A. Di Nola.
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Ji, W. Hyper-operations in effect algebras. Soft Comput 23, 4585–4592 (2019). https://doi.org/10.1007/s00500-018-3372-x
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DOI: https://doi.org/10.1007/s00500-018-3372-x