This paper attempts an exposition of the connection between valuation theory and hyperstructure theory. In this regards, by considering the notion of totally ordered canonical hypergroup we define a hypervaluation of a hyperfield onto a totally ordered canonical hypergroup and obtain some related basic results.
MotivationThe theory of valuations was started in 1912 by the Hungarian mathematician J. Kürschák [24]. Kürschák introduced the concept of a valuation of a field, as being real valued functions on the set of nonzero elements of the field, satisfying certain properties.
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