A Note on Semiprime Hyperideal in Ternary Hypersemirings

Authors

  • M. Salim Darjeeling Govt. College, Department of Mathematics, 19, Lebong Cart Road, Darjeeling, West Bengal, Pin- 734101, India
  • B. Dutta Darjeeling Govt. College, Department of Mathematics, 19, Lebong Cart Road, Darjeeling, West Bengal, Pin- 734101, India

DOI:

https://doi.org/10.3329/jsr.v16i2.67789

Abstract

This research aims to define and investigate the properties of semiprime hyperideals in ternary hypersemirings. The researchers introduce the notion of semiprime hyperideal in a ternary hypersemiring and characterize it. The study has expanded by introducing the ideas of weak n-system and strong n-system in a ternary hypersemiring, and using these; the researchers characterize semiprime hyperideals. Again, the researchers introduce the prime radical β(I) of a hyperideal I in a ternary hypersemiring and obtain the important result that for a proper hyperideal  of a ternary hypersemiring R, β(I) ={r ∈ R: every weak m-system in R which contains rhas a nonempty intersection with I}. Finally, the work has been concluded by introducing the concept of fully idempotent ternary hypersemirng, and using this concept. It has been proved that if S is a commutative ternary hypersemiring with hyperidentity, then S is a regular commutative ternary hypersemiring with hyperidentity.

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Published

2024-05-01

How to Cite

Salim , M., & Dutta, B. (2024). A Note on Semiprime Hyperideal in Ternary Hypersemirings. Journal of Scientific Research, 16(2), 459–469. https://doi.org/10.3329/jsr.v16i2.67789

Issue

Section

Section A: Physical and Mathematical Sciences