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Cantor–Bernstein Theorem for Pseudo-BCK-Algebras

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Abstract

We prove that if A and B are orthogonally σ-complete commutative pseudo-BCK-algebras such that A is isomorphic to a direct factor in B, and also B is isomorphic to a direct factor in A, then A and B are isomorphic. As a consequence we obtain previously known results for MV-algebras (by De Simone, Mundici and Navara), pseudo-MV-algebras (by Jakubík) and lattice-ordered groups (again by Jakubík).

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Authors and Affiliations

  1. Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00, Olomouc, Czech Republic

    Jan Kühr

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  1. Jan Kühr
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Correspondence to Jan Kühr.

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Supported by the Research and Development Council of the Czech Government, the research project MSM 6198959214.

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Kühr, J. Cantor–Bernstein Theorem for Pseudo-BCK-Algebras. Int J Theor Phys 47, 212–222 (2008). https://doi.org/10.1007/s10773-007-9465-4

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  • DOI: https://doi.org/10.1007/s10773-007-9465-4

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