NEW FUNDAMENTAL RELATIONS IN HYPERRINGS AND THE CORRESPONDING QUOTIENT STRUCTURES
In this article, we introduce and analyze the smallest equivalence binary relation $\chi ^{*}$ on a hyperring $R$ such that the quotient $R/\chi ^{*}$, 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 $\sigma^{*}_{p}$ such that the quotient structure is a $p$-ring. Moreover, we introduce a new strongly regular relation $\sigma^{*}_{p}$ such that the quotient structure is a $p$-ring.