A note on hyperrings and hypermodules

Abstract

The main purpose of this paper is to study the concept of the hyperring (ℕ, ⊕, ·), where m ⊕ n = {m + n, k | min{m,n} + k = max{m,n}}, for all m, n ∈ N and the operation · is the usual multiplication in ℕ. In particular, we prove that this hyperring (ℕ, ⊕, ·) is isomorphic to Krasner’s quotient hyperring Z/G in [10]. Moreover, we construct the hyperstructure (ℕ_m, ⊕_m, ·), which is a class of examples of hypermodules and hyperrings.