Basic notions and properties of ordered semihyperrings

Abstract

In this paper, we introduce the concept of semihyperring $(R,+,cdot)$ together with a suitable partial order $le$. Moreover, we introduce and study hyperideals in ordered semihyperrings. Simple ordered semihyperrings are defined and its characterizations are obtained. Finally, we study some properties of quasi-simple and $B$-simple ordered semihyperrings.

Keywords

• ordered semihyperring
• hyperideal
• simple
• quasi-simple
• $B$-simple