Hyperideal theory in ordered Krasner hyperrings

In this paper, we study some properties of ordered Krasner hyper-rings. Also we state some definitions and basic facts and prove some results on ordered Krasner hyperring (R, +, ·, ≤). In particular, we introduce the concepts of prime hyperideals and semiprime hyperideals of an ordered Krasner hyperring and present several examples of them.