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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 4

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

S. RASOULI
D. HEIDARI
B. DAVVAZ
Sayfa
461–469
Yayın Tarihi
2022-10-18
DOI
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Finally, we state conditions that are equivalent with the transitivity of this relation.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper we consider the notion of hyper implicative bounded BCK- algebras, give some examples and introduce the relation $beta$ on them.
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Temel Bulgular & Veri:Then we let $beta^∗$ be the transitive closure of $beta$ .
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Sonuç & Katkı:Finally, we state conditions that are equivalent with the transitivity of this relation.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

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.

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Bu Makaleye Atıf Yap

RASOULI, S., HEIDARI, D., DAVVAZ, B. (2022). $beta$-relations on implicative bounded hyper BCK-algebras. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 4, 461–469. https://ajindex.com/articles/530674

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Kaynakça (9)

  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
  5. 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
  6. Marty, F. Sur une generalization de la notion de groupe, 8iem congres Math. Scandinaves, Stockholm, 45–49, 1934
  7. Spartalis, S. and Vougiouklis, T. The fundamental relations on Hv-rings, Riv. Mat. Pura Appl. 13, 7–20, 1994
  8. Traczyk, T. On the variety of bounded commutative BCK-algebras, Math. Japonica 24, 283–292, 1979
  9. Vougiouklis, T. Hyperstructures and their representations (Hadronic Press, Inc, 115 Palm Harber, USA, 1994).