Abstract
Abstract The α* -relation is a fundamental relation on hyperrings, being the smallest strongly regular relation on hyperrings such that the quotient structure R/α* is a commutative ring. In this paper we introduce on hyperrings the relation ζ m , which is smaller than α*, and show that, on a particular class of m-idempotent hyperrings R, it is the smallest strongly regular relation such that the quotient ring R/ζ * m is commutative. Some properties of this new relation and its differences from the α* -relation are illustrated and discussed. Finally, we show that ζ m is a new representation for α* on this particular class of m-idempotent hyperrings.
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