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Pseudo Weak Effect Algebras and Pseudo Weak D-posets

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Abstract

Pseudo weak effect algebras are base on an noncommutative, associative and cancellative partial addition, but in general not determined by it. Every pseudo BL-algebra gives rise to a pseudo weak effect algebra.

We introduce two different operations in pseudo weak effect algebras and also in the pseudo weak difference posets. We prove that the pseudo weak effect algebras and the pseudo weak difference posets are the same thing.

We give the exact conditions that an equivalence relation does not only allow the formation of a quotient algebra, but that this quotient is also again a pseudo weak effect algebra.

Last, we show that pseudo BL-effect algebras are subdirect products of linearly ordered ones.

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Authors and Affiliations

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

    Jian-sheng Guo, Yong-ming Li & Yong-jian Xie

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

    Yong-ming Li

Authors
  1. Jian-sheng Guo
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  2. Yong-ming Li
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  3. Yong-jian Xie
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Corresponding author

Correspondence to Jian-sheng Guo.

Additional information

This work is supported by National Science Foundation of China (Grant Nos. 10571112, and 60873119), “TRAPOYT” of China and National 973 Foundation Research Program (Grant No. 2002CB312200), Fundamental Research Funds for the Central Universities (Grant No. GK200902047).

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Guo, Js., Li, Ym. & Xie, Yj. Pseudo Weak Effect Algebras and Pseudo Weak D-posets. Int J Theor Phys 50, 1175–1185 (2011). https://doi.org/10.1007/s10773-010-0506-z

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  • DOI: https://doi.org/10.1007/s10773-010-0506-z

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