On Traczyk’s BCK-sequences
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3054512Utgivelsesdato
2022Metadata
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Originalversjon
10.2478/aupcsm-2022-0004Sammendrag
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.