University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 31 1 2020 03 01 Direct Limit of Krasner (m, n)-Hyperrings 75 83 74793 10.22059/jsciences.2020.282723.1007418 EN Reza Ameri Department of Mathematics, Faculty of Mathematics, University of Tehran 0000-0001-5760-1788 Ameneh Asadi Department of Mathematics, Payame Noor University, Tehran, Iran Journal Article 2019 06 19 The purpose of this paper is the study of direct limits in category of Krasner (<em>m, n</em>)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (<em>m, n</em>)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (<em>m, n</em>)-hyperring R such that the quotient space is an (<em>m, n</em>)-ring, to introduce the fundamental functor from category of Krasner (<em>m, n</em>)-hyperrings to the  category of (<em>m, n</em>)-rings. Finally, we study the relationship between fundamental functor and direct limit on Krasner (<em>m, n</em>)-hyperrings. In particular, we prove that the fundamental functor is exact and obtain some its basic properties. https://jsciences.ut.ac.ir/article_74793_d9f858d0855db9f08c09e4226a4ea181.pdf