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Congruences and ideals in pseudoeffect algebras

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Abstract

This paper is devoted to congruences and ideals in pseudoeffect algebras. Let I be a normal ideal in a pseudoeffect algebra E. We show that: (1) the relation ~ I induced by I is a congruence if and only if for every a∈E, I∩ [0,a] is upper directed; (2) the relation ~ I induced by I is a strong congruence if and only if I is a normal weak Riesz ideal in a pseudoeffect algebra E. Moreover, we introduce a stronger concept of congruence—namely Riesz strong congruence—and we prove that, if I is a normal weak Riesz ideal in a pseudoeffect algebra E, then ~ I is a Riesz strong congruence and, conversely, if ~ is a Riesz strong congruence, then I =  [0]~ is a normal weak Riesz ideal, and ~ I = ~.

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Authors and Affiliations

  1. Department of Mathematics, Shaanxi Normal University, 710062, Xi’an, People’s Republic of China

    Hai-Yang Li & Sheng-Gang Li

  2. School of Science, Xi’an Polytechnic University, 710048, Xi’an, People’s Republic of China

    Hai-Yang Li

Authors
  1. Hai-Yang Li
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  2. Sheng-Gang Li
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Correspondence to Hai-Yang Li.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10271069).

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Li, HY., Li, SG. Congruences and ideals in pseudoeffect algebras. Soft Comput 12, 487–492 (2008). https://doi.org/10.1007/s00500-007-0209-4

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  • DOI: https://doi.org/10.1007/s00500-007-0209-4

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