Fundamental Commutative (m, n)-rings Obtained from (m, n)-hyperrings

We introduce the fundamental relation, α∗, on an (m,n)-hyperring R and indicate that this relation is the smallest strongly regular equivalence relation on R such that R/α∗ is an commutative (m,n)-ring. We use α∗-relation to construct the fundamental functor from category of (m,n)-hyperrings to the category of commutative (m,n)-rings. Finally, some necessary and sufficient conditions for transitivity of α are given.