On Traczyk’s BCK-sequences
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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 a˚rmative for n = 1, 2. Nonetheless, by providing counterexamples, we proved that the answers to both those open problems are negative.
Language: English
Page range: 43 - 49
Submitted on: Mar 7, 2022
Accepted on: Aug 10, 2022
Published on: Sep 25, 2022
Published by: Pedagogical University of Cracow
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
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© 2022 Denis Zelent, published by Pedagogical University of Cracow
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