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arXiv · 2306.12426

On Traczyk's BCK-sequences

Denis Zelent
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Abstract

BCK-sequences and n-commutative BCK-algebras were introduced by T. Traczyk, together with two related problems. The first one, whether BCK-sequences are always prolongable. The second one, if the class of all n-commutative BCK-algebras is characterised by one identity. W. A. Dudek proved that the answer to the former question is positive in some special cases, e.g. when BCK-algebra is linearly ordered. T. Traczyk showed that the answer to the latter is affirmative for n = 1, 2. Nonetheless, by providing counterexamples, we proved that the answers to both those open problems are negative.

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Denis Zelent. 2023-03-22. On Traczyk's BCK-sequences. https://doi.org/10.2478/aupcsm-2022-0004

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