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E-perfect effect algebras

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Abstract

The definition of E-perfect effect algebras is introduced, and their structure is studied. We study the lexicographical product of an effect algebra with any upwards directed partially ordered Abelian group, and we show that every E-perfect effect algebra is isomorphic with such a kind of the lexicographical product.

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Acknowledgments

This work was supported by the National Science Foundation of China (Grant No. 60873119) and the Fundamental Research Funds for the Central Universities (Grant No. GK200902047). The authors are indebted to professor A. Dvurečenskij and the referees for corrections of the manuscript. Especially, the referees suggested us to simplify the proof of Theorem 3.4.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Yongjian Xie & Yongming Li

  2. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 81473, Bratislava, Slovakia

    Yongjian Xie

  3. College of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Yongming Li

  4. College of Science, Xi’an University of Science and Technology, Xi’an, 710054, China

    Aili Yang

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  1. Yongjian Xie
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  2. Yongming Li
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  3. Aili Yang
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Correspondence to Yongjian Xie.

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Xie, Y., Li, Y. & Yang, A. E-perfect effect algebras. Soft Comput 16, 1923–1930 (2012). https://doi.org/10.1007/s00500-012-0865-x

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  • DOI: https://doi.org/10.1007/s00500-012-0865-x

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