In this manuscript, we introduce the concept of an atomic subset of the hyper BCK-algebra and study its properties. Also, we give a characterization of the atomic hyper BCK-algebra and show that there are exactly (up to isomorphism) n atomic hyper BCK-algebras H with |H| = n for any natural number n.
hyper BCK-algebra;atomic subset and atomic hyper BCK-algebra;
R. A. Borzooei and H. Harizavi, Regular congruence relations on Hyper BCK-algebras, Scientiae Mathematicae Japonicae 61 (2005), no. 1, 83–97
Y. Imai and K. Is´eki, On axiom systems of propositional calculi XIV, Proc. Japan Academy 42 (1966), 19–22
Y. B. Jun, X. L. Xin, E. H. Roh, and M. M. Zahedi, Strong hyper BCK-ideals of hyper BCK-algebra, Mathematicae Japonicae, Vol. 51 (2000), no. 3, 493–498
Y. B. Jun, M. M. Zahedi, X. L. Xin, and R. A. Borzooei, On hyper BCK-algebra, Italian Journal of Pure and Applied Mathematics, Oxford Ser. 10 (2000), 127–136