On Regular Γ-semihyperrings and Idempotent Γ-semihyperrings

• Published in: Kyungpook mathematical journal pp. 35 - 45
• Main Authors: Kishor Fakira Pawar, Jitendra Jaysing Patil
• Format: Journal Article
• Language: English
• Published: 경북대학교 자연과학대학 수학과 01.03.2019
• Subjects: 수학
• ISSN: 1225-6951; 0454-8124
• DOI: 10.5666/KMJ.2019.59.1.35

The Γ-semihyperring is a generalization of the concepts of a semiring, a semihyperring and a Γ-semiring. Here, the notions of (strongly) regular Γ-semihyperring, idempotent Γ-emihyperring; invertible set, invertible element in a Γ-semihyperring are introduced, and several examples given. It is proved that if all subsets of Γ-semihyperring are strongly regular then for every Δ⊆ Γ, there is a Δ-idempotent subset of R. Regularity conditions of Γ-semihyperrings in terms of ideals of Γ-semihyperrings are also characterized. KCI Citation Count: 0