NEW FUNDAMENTAL RELATIONS IN HYPERRINGS AND THE CORRESPONDING QUOTIENT STRUCTURES
نویسندگان
1 Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.
2 Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.
3 Department of Mathematical Sciences, Yazd University, Yazd, Iran.
doi
10.22044/jas.2022.10071.1501چکیده
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.
