new fundamental relations in hyperrings and the corresponding quotient structures

In this article, we introduce and analyse the smallest equivalence binary relation χ ∗ on a hyperring r such that the quotient r/χ∗ , the set of all equivalence classes, is a commutative ring with identity and of characteristic m. the characterizations of commutative rings with identity via strongly regular relations is investigated and some properties on the topic are presented. moreover, we introduce a new strongly regular relation σ ∗ p such that the quotient structure is a p-ring.