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,

α^{*}

, on an

(m, n)

-hyperring

R

and indicate that this relation is the smallest strongly regular equivalence relation on

R

such that

R / α^{*}

is an commutative

(m, n)

-ring. We use

α^{*}

-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

α

are given.

Keywords