TY - JOUR
AU - Zelent, Denis
PY - 2022/09/05
Y2 - 2023/11/29
TI - On Traczykâ€™s BCK-sequences
JF - Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica
JA - Ann. Univ. Paedagog. Crac. Stud. Math.
VL - 21
IS -
SE - Published
DO -
UR - https://studmath.up.krakow.pl/article/view/9499
SP - 43-49
AB - <p>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.</p>
ER -