Some Studies on Ordered Krasner Hyperrings with Respect to Derivations

Abstract

The concept of ordered Krasner hyperrings is a generalization of the concept of ordered rings. In this paper, we study subhyperrings, d-subhyperrings and injective subhyperrings of ordered Krasner hyperrings. Also, the notion of convex ordered Krasner hyperrings is introduced and some related results are studied. Moreover, we prove that for an injective strong derivation d of a convex ordered Krasner hyperring (R,+,.,≤) associated to a d-strongly regular relation σ, there exists an injective strong derivation on (R/σ,⨁;⨀;≼).

Key words and phrases. Ordered Krasner hyperring, subhyperring, derivation.

2000 Mathematics Subject Classification. 16Y99, 20N20