Abstract
Using the unitizations of symmetric-generalized pseudo-effect algebras, we investigate the relationships between the maximal compatible sets in a prelattice symmetric-generalized pseudo-effect algebra and the maximal compatible sets in its unitization. We also prove that a symmetric-generalized pseudo-effect algebra is a symmetric-generalized pseudo MV-effect algebra if and only if its unitization is a symmetric pseudo MV-effect algebra.
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Acknowledgments
This work was supported partially by the Fundamental Research Funds for the Central Universities (Grant No. GK201002037), and a research grant from the Education Department of Shaanxi Province (Grant No. 12JK0875). We are sincerely grateful to anonymous referees for their various valuable suggestions to improve the readability of our paper. Especially, we are greatly indebted to the referees for their suggestions for the proof of Theorem 4.11(iii).
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Communicated by A. Dvurečenskij.
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Yang, A., Xie, Y. Prelattice-generalized pseudo-effect algebras. Soft Comput 19, 1135–1141 (2015). https://doi.org/10.1007/s00500-014-1540-1
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DOI: https://doi.org/10.1007/s00500-014-1540-1