On Traczyk's BCK-sequences
Rings and Algebras
2023-06-23 v1 Logic
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.
Cite
@article{arxiv.2306.12426,
title = {On Traczyk's BCK-sequences},
author = {Denis Zelent},
journal= {arXiv preprint arXiv:2306.12426},
year = {2023}
}