In this paper, we introduce and analyze the smallest equivalence binary relation $$ \eta_{1,m}^{*} $$ η 1 , m ∗ on a hyperring R such that the quotient $$ R/\eta_{1,m}^{*}$$ R / η 1 , m ∗ , the set of all equivalence classes, is a commutative ring with identity and for any x ∊ R, $$ [\eta_{1,m}^{*} (x)]^{m + 1} = \eta_{1,m}^{*} (x) $$ [ η 1 , m ∗ ( x ) ] m + 1 = η 1 , m ∗ ( x ) . The characterization of Boolean rings via strongly regular relations is investigated, and some properties on the topic are presented.