On bi-ideals of Γ-semihyperrings

Document Type : Research Paper

Authors

1 Department of Mathematics, Indraraj Arts, Commerce and Science college, Sillod, Dr. Babashasheb Ambedkar Marathwada University Aurangabad- 431 112, India.

2 Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, 425 001 M.S., India

Abstract

The concept of Γ-semihyperrings is a generalization of semirings, semihyperrings and  Γ-semirings. The notion of
bi-ideals and minimal bi-ideals in Γ-semihyperrings is introduced with several examples. We also made some ideal theoretic characterization of bi-ideals and minimal bi-ideals in Γ-semihyperrings. Then the notion of bi-simple
Γ-semihyperrings is introduced and it is proved that ``If R is a Γ-semihyperring without zero, then R is a bi-simple
Γ-semihyperring if and only if (k)b=R, for all k∈ R, where (k)b is a bi-ideal generated by k."
 

Keywords

References

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Journal of Hyperstructures
Volume 11, Issue 2
December 2022
Pages 183-195

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