A note on hyperrings and hypermodules

The main purpose of this paper is to study the concept of the hyperring (N,circle plus,), where m circle plus n = {m+n, k| min {m, n}+k= max {m, n}}, for all m, n is an element of N and the operation is the usual multiplication in N. In particular, we prove that this hy-perring (N,circle plus,) is isomorphic to Krasner's quotient hyperring (Z)/(G) in [10]. Moreover, we construct the hyper structure (N-m,circle plus(m),), which is a class of examples of hyper modules and hyperrings.