نشریه علوم ریاضی و انفورماتیک

We study the concept of hypervaluations on hyperfields. The main aim of this paper is to show that any hypervaluation from a hyperfield onto an ordered canonical hypergroup is the composition of a hypervaluation onto an ordered abelian group (which induces the same valuation hyperring) and an order preserving homomorphism of hypergroups. This implies that the generalization of hypervaluations proposed in [13] can be reduced to the original definition of hypervaluation given by Davvaz and Salasi in [4]. Moreover, we provide counterexamples to some assertions which appear in [13].