Hyperrings with n-ary composition hyperoperation

Based on the concepts of composition ring and composition hyperring, in this note, we introduce the notion of [Formula: see text]-ary composition hyperring and study the connections with composition hyperrings. Moreover, we show that special strong multiendomorphisms of hyperrings can determine the [Formula: see text]-ary composition structure of a such hyperring and also a subclass of [Formula: see text]-ary composition hyperrings. Finally, the three isomorphism theorems are studied in the framework of [Formula: see text]-ary composition hyperrings.