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Weak Commutative Pseudoeffect Algebras

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Abstract

As noncommutative generalizations of effect algebras, we introduce weak commutative pseudoeffect algebras. In this paper, we prove that the generalized pseudoeffect algebras can be unitized if and only if they are weak commutative. Then we discuss the relationships between weak commutative pseudoeffect algebras and weak commutative generalized pseudoeffect algebras. We prove that the category of weak commutative pseudoeffect algebras is a reflective subcategory of weak commutative generalized pseudoeffect algebras. Similarly, we introduce weak commutative pseudodifference posets and show the relationships between weak commutative pseudoeffect algebras and weak commutative pseudodifference posets.

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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, Jiansheng Guo & Fang Ren

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

    Yongming Li

  3. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316004, China

    Dechao Li

Authors
  1. Yongjian Xie
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  2. Yongming Li
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  3. Jiansheng Guo
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  4. Fang Ren
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  5. Dechao Li
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Correspondence to Dechao Li.

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Xie, Y., Li, Y., Guo, J. et al. Weak Commutative Pseudoeffect Algebras. Int J Theor Phys 50, 1186–1197 (2011). https://doi.org/10.1007/s10773-010-0515-y

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  • DOI: https://doi.org/10.1007/s10773-010-0515-y

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