On some strongly regular relations on hyperrings

In this paper first by the fact that the relation ${\alpha }^{\ast }$ is the transitive closure of two its subrelations we introduce and analyze a binary relation ${\lambda }_e^{\ast }$ 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 ${\mathrm{\Lambda }}^{\ast }$ such that its derived ring be a unitary commutative ring.