$beta$-relations on implicative bounded hyper BCK-algebras

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

In this paper we consider the notion of hyper implicative bounded BCK- algebras, give some examples and introduce the relation $beta$ on them. Then we let $beta^∗$ be the transitive closure of $beta$ . In hyper implicative bounded BCK-algebra theory, the fundamental relation is defined as the smallest equivalence relation so that the quotient would be the (fundamental) BCK-algebra. We show that$beta^∗$ is the fundamental re- lation on a hyper implicative bounded BCK-algebra. Finally, we state conditions that are equivalent with the transitivity of this relation.

PDF

___

[1] Cornish, W.H. On Iseki’s BCK-algebras, algebraic structures and applications (Proceedings of the First Western Australian Conference on Algebra (eds. P. Schultz, C.E. Praeger and R.P. Sullivan), Marcel Dekker, New York, 1982), 101–122.
[2] Corsini, P. Prolegomena of hypergroup theory (Aviani Editore, Tricesimo, 1993).
[3] Imai, Y. and Iseki, K. On axiom systems of propositional calculi XIV, Proc. Japan Academy 42, 26–29, 1966.
[4] Iseki, K. and Tanaka, S. Ideal theory BCK-algcbras, Math. Japonica 21, 351–366, 1976.
[5] lseki, K. and Tanaka, S. An introduction to the theory of BCK-algebras, Math. Japonica 23, 1–26, 1978.
[6] Jun, Y.B., Zahedi, M.M., Xin, X. L. and Borzoei, R.A. On hyper BCK-algebras, Italian Journal of Pure and Applied Mathematics 8, 127–136, 2000.
[7] Marty, F. Sur une generalization de la notion de groupe, 8iem congres Math. Scandinaves, Stockholm, 45–49, 1934.
[8] Spartalis, S. and Vougiouklis, T. The fundamental relations on Hv-rings, Riv. Mat. Pura Appl. 13, 7–20, 1994.
[9] Traczyk, T. On the variety of bounded commutative BCK-algebras, Math. Japonica 24, 283–292, 1979.
[10] Vougiouklis, T. Hyperstructures and their representations (Hadronic Press, Inc, 115 Palm Harber, USA, 1994).