HYPERABSOLUTE VALUES IN HYPERFIELDS : CONNECTIONS TO HYPERVALUATION

Abstract

In this paper, we attempt an exposition of the connection between absolutevalue and hyperstructure theory. We define the hyperabsolute value of a hyperfield andinvestigate its properties. Moreover, we introduce the notion of a hypermetric space and useit to find a necessary and sufficient condition for two hyperabsolute values of a hyperfield to be equivalent. Finally, we explore the relationship between hyperabsolute values of ahyperfield and its hypervaluations.