Real Closed Graded Fields

Abstract

We investigate homogeneous orderings on G-graded rings where G is an arbitrary ordered abelian group. For this we introduce the notion of real closed graded fields. We generalize the Artin-Schreier characterization of real closed fields to the graded context. We also characterize real closed graded fields in terms of the group G and in terms of its homogeneous elements of degree 0.