Affiliation:
1. Department of Mathematics, Faculty of Basic Sciences , University of Bojnord , Bojnord , Iran
2. Centre for Information Technologies and Applied Mathematics , University of Nova Gorica , Nova Gorica , Slovenia
Abstract
Abstract
On a general hyperring, there is a fundamental relation, denoted γ
*, such that the quotient set is a classical ring. In a previous paper, the authors defined the relation εm
on general hyperrings, proving that its transitive closure
ε
m
∗
$\begin{array}{}
\displaystyle
\varepsilon^{*}_{m}
\end{array}$
is a strongly regular equivalence relation smaller than the γ
*-relation on some classes of hyperrings, such that the associated quotient structure modulo
ε
m
∗
$\begin{array}{}
\displaystyle
\varepsilon^{*}_{m}
\end{array}$
is an ordinary ring. Thus, on such hyperrings,
ε
m
∗
$\begin{array}{}
\displaystyle
\varepsilon^{*}_{m}
\end{array}$
is a fundamental relation. In this paper, we discuss the transitivity conditions of the εm
-relation on hyperrings and m-idempotent hyperrings.
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