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ON A CERTAIN GENERALIZATION OF POLYGROUPS BY E-POLYGROUPS

  • Akbar Dehghan Nezhad (School of Mathematics and Computer Science, Iran University of Science and Technology) ;
  • Bijan Davvaz (Department of Mathematics, Yazd University)
  • Received : 2024.03.21
  • Accepted : 2024.08.20
  • Published : 2024.12.20

Abstract

In this paper, first we generalize the notion of polygroups and weak polygroups by the notion of E-polygroups and weak E-polygroups. Then, we study the isomorphism theorems on E-polygroups and weak E-polygroups. Finally, the fundamental relations on weak E-polygroups are investigated.

Keywords

Acknowledgement

The author thank the referee for reading of the manuscript carefully. Also, the authors would like to thank the anonymous referees for their constructive comments.

References

  1. M. Al-Tahan, B. Davvaz, P. Harikrishnan, and P. Pallavi, Subpolygroup commutativity degree of finite extension polygroup, Internat. J. Algebra Comput. 34 (2024), no. 1, 55-68. 
  2. S. D. Comer, Polygroups derived from cogroups, Journal of Algebra 89 (1984), no. 2, 397-405. 
  3. P. Corsini, Prolegomena of Hypergroup Theory, Second edition, Aviani Editor, 1993.
  4. P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers, 2003. 
  5. B. Davvaz, On polygroups and weak polygroups, Southeast Asian Bull. Math. 25 (2012), 87-95. 
  6. B. Davvaz, Polygroup Theory and Related Systems, World Scientific Publishing Co. Pte. Ltd., 2013. 
  7. B. Davvaz and T. Vougiouklis, A Walk Through Weak Hyperstructures- Hv-Structure, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2019. 
  8. B. Davvaz and I. Cristea, Fuzzy Algebraic Hyperstructures-An Introduction, Springer, 2015. 
  9. B. Davvaz and V. Leoreanu-Fotea, Krasner Hyperring Theory, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2024. 
  10. A. Linzi, Polygroup objects in regular categories, AIMS Math. 9 (2024), no. 5, 11247-11277. 
  11. F. Marty, Sur une generalization de la notion de group, 8th Congress Math. Scandenaves, Stockholm, 45-49, 1934. 
  12. E. Mohammadzadeh and F. Mohammadzadeh, On nilpotent and solvable pair of polygroups, J. Algebr. Hyperstruct. Log. Algebras 2 (2021), no. 2, 1-12. 
  13. A. C. Sonea, New aspects in polygroup theory, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 28 (2020), no. 3, 241-254. 
  14. T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Inc, 115, Palm Harber, USA, 1994.