A Note on Semiprime Hyperideal in Ternary Hypersemirings - Salim , M.; Dutta, B. (Journal of Scientific Research, 2024)
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.