On σ-derivations of Krasner hyperrings

Abstract

We present a significant extension of the derivation concept to Krasner hyperrings, namely the σ-derivation, which is defined utilizing a self-mapping σ on the hyperring R. We investigate several important properties of these σ-derivations and explore their behavior in prime Krasner hyperrings. Furthermore, we establish conditions under which a Krasner hyperring becomes commutative.