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Filters of implication reducts of basic algebras

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Abstract

Since basic algebras were introduced as a common generalization of MV-algebras and orthomodular lattices, their implication reducts form a common generalization of BCK-algebras and orthoimplication algebras introduced by J. C. Abbott. As shown in our previous paper, congruences in these implication reducts are in a one-to-one correspondence with their kernels. Hence, to characterize congruences it is enough to describe its kernels which is done in the paper.

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Authors and Affiliations

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

    Ivan Chajda

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  1. Ivan Chajda
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Correspondence to Ivan Chajda.

Additional information

Communicated by A. DvureÄenskij.

This work was supported by the project CZ.1.07/2.3.00/20.0051 Algebraic Methods in Quantum Logic.

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Chajda, I. Filters of implication reducts of basic algebras. Soft Comput 18, 849–852 (2014). https://doi.org/10.1007/s00500-013-1200-x

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