On Different Definitions of Hyper Pseudo BCC-algebras

Year 2023, , 56 - 65, 31.07.2023

Didem Sürgevil Uzay , Alev Fırat

https://doi.org/10.54974/fcmathsci.1145287

Abstract

We study hyper pseudo BCC-algebras which are a common generalization of hyper BCC-algebras and hyper BCK-algebras. In particular, we introduce different notion of hyper pseudo BCC-algebras and describe the relationship among them. Then, by choosing one of these definitions, we investigate for its related properties.

Keywords

hyper pseudo order, hyper operation, hyper pseudo BCC-algebras

References

• Borzooei R.A., Dudek W.A., Koohestani N., On hyper BCC-algebras, International Journal of Mathematics and Mathematical Sciences, 1-18, 2006.
• Borzooei R.A., Rezazadeh A., Ameri R., On hyper pseudo BCK-algebras, Iranian Journal of Mathematical Sciences and Informatics, 9(1), 13-29, 2014.
• Dudek W.A., On BCC-algebras, Logique & et Analyse Nouvelle Série, 33(129-130), 103-111, 1990.
• Iseki K., Tanaka S., An introduction to the theory of BCK-algebras, Mathematica Japonica, 23, 1-26, 1978.
• Jun Y.B., Zahedi M.M., Xin X.L., Borzooei R.A., On hyper BCK-algebras, Italian Journal of Pure and Applied Mathematics, 8, 127-136, 2000.
• Komori Y., The class of BCC-algebras is not a variety, Mathematica Japonica, 29(3), 391-394, 1984.
• Marty F., Sur une generalization de la notion de groupe, In Eighth Congress Math. Scandinaves, 45-49, 1934.