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

Document Type: Research articles


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


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.


Article Title [Persian]

حلقه های (m,n)-تایی تعویض پذیر اساسی بدست آمده از ابرحلقه های (m, n)-تایی