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On Traczyk's BCK-sequences

From MaRDI portal
Publication:6441043

DOI10.2478/AUPCSM-2022-0004arXiv2306.12426MaRDI QIDQ6441043

Author name not available (Why is that?)

Publication date: 22 March 2023

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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