Hyperrings which every element is sum of an idempotent and nilpotent

Abstract

In this paper, we define a generalized of clean of Krasner hyperrings for general hyperrings based on the notation of nilpotent elements of a general hyperring R, named nil clean hyperring. We examine characterization of this kind of hyperrings and finally, we obtain some relations of nil clean general hyperrings with other hyperrings.