On hyper Z-algebras

Sahar Jaafar  Mahmood; Dhirgam Allawy  Hussein

doi:10.24297/jam.v21i.9271

Authors

Sahar Jaafar Mahmood Department of Multimedia, College of Computer Science and Information Technology, University of AlQadisiyah, P.O. Box 88, Al Diwaniyah, Al-Qadisiyah, Iraq, sahar.jaafar@qu.edu.iq.
Dhirgam Allawy Hussein Directorate of Education in Al-Qadisiyah , Diwaniyah , Iraq, dhirgam.allawy@qu.edu.iq

DOI:

https://doi.org/10.24297/jam.v21i.9271

Keywords:

hyperZ- homomorphism, strong hyper Z-ideal , weak hyper Z-ideal, hyper Z-subalgebra, hyper Z-algebra, Z-algebra

Abstract

This study introduces the concept of hyperZ-algebra and investigates its features. In addition, we establish and prove a number of theorems about the relation between (Ṟ-ḧZ , Ḉ-ḧZ , Ḓ-ḧZ , Ṱ-ḧZ , Ṿ-ḧZ ). Moreover, we explain the hyper subalgebra ,a weakhyper Z-ideal and a stronghyper Z-ideal, as well as their relationship. Finally, the hyperhomomorphism Z-algebra is constructed and the isomorphism theorems are examined.

Downloads

Download data is not yet available.

References

F. Marty, Sur une generalization de la notion de group, 8th Congress Math. Scandinaves,Stockholm, (1934), 45{49.

P. Corsini, Prolegomena of hypergroup theory, (Second Edition), Aviani Editor, 1993.

Y.B. Jun, M.M. Zahedi, X.L. Xin, R.A. Borzooei, On hyper BCK-algebras, Italian Journal of Pure and Applied Mathematics, 8 (2000), 127-136.

R.A. Borzooei, A. Hasankhani, M.M. Zahedi, Y.B. Jun, On hyper K-algebras, Japanese Journal of Mathematics, 52(1) (2000), 113-121.

X.L. Xin, Hyper BCI-algebras, Discuss Mathematics Society, 26 (2006), 5-19.

R.A. Borzooei, W.A. Dudek, N. Kouhestani, On hyper BCC-algebras, International Journal of Mathematics and Mathematical Sciences, (2006), 1-18. DOI:org/10.1155/IJMMS/2006/49703

J.C. Endam, On hyper B-Algebras, Dissertation, MSU-IIT, 2019.

A.L.O. Vicedo, J.P. Vilela, Hyper B-ideals in hyper B-algebra, Journal of Ultra Scientist of Physical Sciences, 29(8) (2017), 339-347. DOI: 10.22147/jusps-A/290805

S.Niazian, On hyper BI-algbras , JAHLA ,vol(2),N(1)(2021),P 47-67. DOI:10.52547/HATEF.JAHLA.2.1.4

Chandramouleeswaran M., Muralikrishna P., Sujatha K. and Sabarinathan S., A note on Z-algebra, Italian Journal of Pure and Applied Mathematics-N.38, 707–714 (2017). Google Scholar.