# Fundamental commutative (m, n)-rings obtained from (m, n)-hyperrings

Document Type: Research articles

Authors

1 Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran

2 School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran

10.22080/cjms.2019.15921.1379

Abstract

We introduce the fundamental relation, $\alpha^{*}$, on an $(m,n)$-hyperring $R$ and indicate that this relation is the smallest strongly regular equivalence relation on $R$ such that $R/\alpha^{*}$ is an commutative $(m, n)$-ring. We use $\alpha^{*}$-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 $\alpha$ are given.

Keywords

Article Title [Persian]