Document Type: Original Paper


1 Department of Mathematics, Faculty of Mathematics, University of Tehran

2 Department of Mathematics, Payame Noor University, Tehran, Iran


The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (m, n)-hyperring R such that the quotient space is an (m, n)-ring, to introduce the fundamental functor from category of Krasner (m, n)-hyperrings to the  category of (m, n)-rings. Finally, we study the relationship between fundamental functor and direct limit on Krasner (m, n)-hyperrings. In particular, we prove that the fundamental functor is exact and obtain some its basic properties.