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

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

Caspian Journal of Mathematical Sciences
Volume 8, Issue 2 - Serial Number 2
August 2019
Pages 162-177

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