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.