Non-Commutative Hypervaluation on Division Hyperrings

In this paper, the notion of a non-commutative hypervalu- ation as a generalization of a non-commutative valuation is introduced and some results are proved in this respect. Also, we define the notion of a non-commutative hypervaluation over a Krasner hyperfield and some basic results and characterizations are obtained. Finally, we introduce the non-commutative discrete hypervaluation of a hyperfield and inves-tigate the important properties.