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Real Closed Graded Fields

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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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References

  1. Anderson, M., Feil, T.: Lattice-Ordered Groups. An Introduction. D. Reidel, Dordrecht (1988)

  2. Becker, E., Berr, R., Gondard, D.: Valuation fans and residually real closed henselian fields. J. Algebra 215, 574–602 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Boulagouaz, M.: An introduction to the Galois theory for graded fields. Algebra and number theory. Lect. Notes Pure Appl. Math. 208, 21–31 (2000)

    MathSciNet  Google Scholar 

  4. Bourbaki, N.: Algebra I. Springer, Berlin (1989)

    MATH  Google Scholar 

  5. Bourbaki, N.: Commutative Algebra. Springer, Berlin (1989)

    MATH  Google Scholar 

  6. Kaiser, R.: Das sphärische Spektrum eines graduierten Ringes. Regensbg. Math. Schr. 27 (1998)

  7. Knebusch, M., Scheiderer, C.: Einführung in die reelle Algebra. Vieweg, Braunschweig (1989)

    MATH  Google Scholar 

  8. Nǎstǎsescu, C., von Oystaeyen, F.: Graded ring theory. N.-Holl. Math. Libr. 28 (1982)

  9. Prestel, A., Delzell, C.N.: Positive Polynomials. Springer, Berlin (2001)

    MATH  Google Scholar 

  10. Robinson, D.J.S.: A Course in the Theory of Groups. Springer, New York (1982)

    MATH  Google Scholar 

  11. Stengle, G., Yousef, H.: The spherical spectrum of a graded ring. Geom. Dedic. 52, 195–208 (1994)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Tobias Kaiser.

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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

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