On hyperideals of Krasner hyperrings based on derived unitary rings

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

2 Mathematics Department, Vali-e-Asr University of Rafsanjan, Rafsanjan,Iran

3 Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran

4 Center for Information Technologies and Applied Mathematics, University of Nova Gorica, Slovenia

Abstract

In this paper first, we introduce and analyze the strongly regular relations $\lambda^*_{e}$ and $\Lambda^*_{e}$ on a hyperring such that the derived quotient ring is unitary and unitary commutative, respectively. Next, we define and study the notion of $\lambda_e$-parts in a hyperring and  characterize the $\lambda_e$-parts in a $\lambda_e$-strong hyperring $R$. Finally, we introduce the notion of $\lambda_e$-closed hyperideal in a hyperring and study some of its fundamental properties in Krasner hyperrings.

Keywords

References

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Journal of Mahani Mathematical Research
Volume 11, Issue 3 - Serial Number 23
Special Issue dedicated to Prof. Mashaallah Mashinchi.
November 2022
Pages 33-56

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History

  • Receive Date: 12 January 2022
  • Revise Date: 19 April 2022
  • Accept Date: 29 April 2022

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