University of TehranJournal of Sciences, Islamic Republic of Iran1016-110431120200301Direct Limit of Krasner (m, n)-Hyperrings75837479310.22059/jsciences.2020.282723.1007418ENReza AmeriDepartment of Mathematics, Faculty of Mathematics, University of Tehran0000-0001-5760-1788Ameneh AsadiDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20190619The 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 theĀ 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