Gamma^*-RELATION an‎d CATEGORICAL CONNECTION OF (m; n)-HYPERRINGS an‎d (m; n)-RINGS

Let R be an (m,n)-hyperring. The Γ^* -relation on R in the sense of Mirvakili and Davvaz is the smallest strong compatible relation such that the quotient R/Γ^* is an (m,n)-ring. We use Γ^* -relation to construct a fundamental functor, F from the category of (m, n)-hyperrings to the category of (m,n)-rings. Also we define a functor U from the category of classical (m,n)-rings to the category of (m,n)-hyperrrings. Finally, we give a natural transformation between functors F and U, and we investigate the concept of adjunction for them.