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.
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Supported by DFG-project KN202/5-1.
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Kaiser, T. Real Closed Graded Fields. Order 24, 107–120 (2007). https://doi.org/10.1007/s11083-007-9060-6
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DOI: https://doi.org/10.1007/s11083-007-9060-6