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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 ∗ (...
In this paper, we introduce and analyze a fundamental strongly regular equivalence relation on a hypermodule over a hyperring which is the smallest equivalence relation such that the quotient is cyclic module over a (fundamental) ring. Then we state the conditions that is equivalent with the transitivity of this relation. Finally, a characterization of the derived hypermodule (with canonical hypergroup)...
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