| Summary: | 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
εm∗$\begin{array}{}
\displaystyle
\varepsilon^{*}_{m}
\end{array}$ is a strongly regular equivalence relation smaller than the γ*-relation on some classes of hyperrings, such that the associated quotient structure modulo
εm∗$\begin{array}{}
\displaystyle
\varepsilon^{*}_{m}
\end{array}$ is an ordinary ring. Thus, on such hyperrings,
εm∗$\begin{array}{}
\displaystyle
\varepsilon^{*}_{m}
\end{array}$ 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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