Semihypergroups in Which the Radical of Every Hyperideal Is a Subsemihypergroup

Paper Details

Authors: Sanborisoot J.; Palakawong Na Ayutthaya P.

DOI: 10.28924/2291-8639-24-2026-155

Journal: International Journal of Analysis and Applications

Year: 2026

Publisher: Etamaths Publishing

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 0

Abstract

The concept of a semihypergroup is a notable generalization of the concept of a semigroup. For nonempty subset A of a semihypergroup H, the radical of A denoted by (Formula Presented), is(Formula Presented) = {a ∈ H | an ⊆ A for some positive integer n}. A characterization when the radical of every hyperideal of H is a subsemihypergroup of H is investigated and given in this paper. Indeed, we characterize when the radical of every hyperideal of H is a bi-hyperideal of H; when the radical of every bi-hyperideal of H is a left hyperideal of H; and when the radical of every subsemihypergroup of H is a hyperideal of H. © 2026 the author(s).

Keywords

bi-hyperideal; hyperideal; semihypergroup; subsemihypergroup

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