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On the structure of linearly ordered pseudo-BCK-algebras

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Abstract

Pseudo-BCK-algebras are a non-commutative generalization of well-known BCK-algebras. The paper describes a situation when a linearly ordered pseudo-BCK-algebra is an ordinal sum of linearly ordered cone algebras. In addition, we present two identities giving such a possibility of the decomposition and axiomatize the residuation subreducts of representable pseudo-hoops and pseudo-BL-algebras.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

  2. Department of Algebra and Geometry, Faculty of Science, Palacký University, Tř. 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Jan Kühr

Authors
  1. Anatolij Dvurečenskij
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  2. Jan Kühr
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Correspondence to Jan Kühr.

Additional information

The paper has been supported by the Center of Excellence SAS-Physics of Information-I/2/2005, the grants VEGA Nos 2/6088/26, 2/0032/09, by the Slovak Research and Development Agency under the contract No. APVV-0071-06, Bratislava, and by the Czech Government research project No. MSM6198959214.

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Dvurečenskij, A., Kühr, J. On the structure of linearly ordered pseudo-BCK-algebras. Arch. Math. Logic 48, 771–791 (2009). https://doi.org/10.1007/s00153-009-0151-5

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  • DOI: https://doi.org/10.1007/s00153-009-0151-5

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