<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>BCK-sequences and <italic>n</italic>-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 <italic>n</italic>-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 <italic>n</italic> = 1, 2. Nonetheless, by providing counterexamples, we proved that the answers to both those open problems are negative.</p>
</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.

On Traczyk’s BCK-sequences

Norwegian University of Science and Technology

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"On Traczyk\u2019s BCK-sequences"}

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...

On Traczyk’s BCK-sequences

Published Online: Sep 25, 2022

Page range: 43 - 49

Received: Mar 07, 2022

Accepted: Aug 10, 2022

DOI: https://doi.org/10.2478/aupcsm-2022-0004

Keywords
BCK-algebra, BCK-sequence, variety

© 2022 Denis Zelent, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

On Traczyk’s BCK-sequences

Published Online: Sep 25, 2022

Page range: 43 - 49

Received: Mar 07, 2022

Accepted: Aug 10, 2022

DOI: https://doi.org/10.2478/aupcsm-2022-0004

KeywordsBCK-algebra, BCK-sequence, variety

© 2022 Denis Zelent, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
BCK-algebra, BCK-sequence, variety