A NEW FORM OF γ-RELATION ON SOME HYPERRINGS

In this paper, a new equivalence relation, called 〖ε 〗_m^*on a particular class of hyperrings is introduced. This relation is smaller than γ^*on hyperrings and it is shown that 〖ε 〗_m^* is the smallest strongly regular relation on such hyperrings such that the quotient R/(〖ε 〗_m^* ) is a ring. Moreover, the concept of m-idempotent hyperrings is defined and shown that 〖ε 〗_m^* is a new exhibition for γ^* on them.