On some strongly regular relations on hyperrings

In this paper first by the fact that the relation $\alpha^*$ is the transitive closure of two its subrelations we introduce and analyze a binary relation $\lambda^*_e$ on a hyperring such that the derived ring is a unitary ring. Next we introduce and study the notion of $\lambda_e$-parts in a hyperring and we characterize $\lambda_e$-parts in a $\lambda_e$-strong hyperring $R$. Finally we introduce a new relation $\Lambda^*$ such that its derived ring be a unitary commutative ring.