Have a personal or library account? Click to login
The Space of Real Places on R(x,y) Cover
By: Ron Brown and  Jonathan L. Merzel  
Open Access
|Aug 2018

References

  1. [1] Bourbaki N., Éléments de mathématique. Fasc. XXX. Algèbre commutative. Chapitre 5: Entiers. Chapitre 6: Valuations, Hermann, Paris, 1964.
  2. [2] Brown R., Valuations, primes and irreducibility in polynomial rings and rational function fields, Trans. Amer. Math. Soc. 174 (1972), 451-488.10.1090/S0002-9947-1972-0371872-1
  3. [3] Brown R., Roots of irreducible polynomials in tame Henselian extension fields, Comm. Algebra 37 (2009), 2169-2183.10.1080/00927870802467197
  4. [4] Brown R., Marshall M., The reduced theory of quadratic forms, Rocky Mountain J. Math 11 (1981), 161-175.
  5. [5] Brown R., Merzel J.L., Invariants of defectless irreducible polynomials, J. Algebra Appl. 9 (2010), 603-631.10.1142/S0219498810004130
  6. [6] Dubois D.W., Infinite primes and ordered fields, Dissertationes Math. Rozprawy Mat. 69 (1970), 43 pp.
  7. [7] Engler A.J., Prestel A., Valued fields, Springer-Verlag, New York, 2005.
  8. [8] Harman J., Chains of higher level orderings, in: Dubois D.W., Recio T. (Eds.), Ordered fields and real algebraic geometry, Contemp. Math., 8, Amer. Math. Soc., Providence, 1982, pp. 141-174.10.1090/conm/008/653181
  9. [9] Kaplansky I., Maximal fields with valuations, Duke Math. J. 9 (1942), 303-321.
  10. [10] Khanduja S.K., Khassa R., On invariants and strict systems of irreducible polynomials over Henselian valued fields, Comm. Algebra 39 (2011), 584-593.10.1080/00927871003591934
  11. [11] Knebusch M., On algebraic curves over real closed fields. I, Math. Z. 150 (1976), 49-70.10.1007/BF01213885
  12. [12] Kuhlmann K., The structure of spaces of ℝ-places of rational function fields over real closed fields, Rocky Mountain J. Math. 46 (2016), 533-557.10.1216/RMJ-2016-46-2-533
  13. [13] Kuhlmann K., Kuhlmann F.-V., Embedding theorems for spaces of ℝ-places of rational function fields and their products, Fund. Math. 218 (2012), 121-149.10.4064/fm218-2-2
  14. [14] Lam T.Y., Orderings, valuations and quadratic forms, CBMS Regional Conference Series in Mathematics, 52, Amer. Math. Soc., Providence, 1983.10.1090/cbms/052
  15. [15] MacLane S., A construction for absolute values in polynomial rings, Trans. Amer. Math. Soc. 40 (1936), 363-395.10.1090/S0002-9947-1936-1501879-8
  16. [16] Rosenstein J.G., Linear Orderings, Pure and Applied Mathematics, 98, Academic Press, New York, 1982.
  17. [17] Schülting H.-W., Real points and real places, in: Dubois D.W., Recio T. (Eds.), Ordered fields and real algebraic geometry, Contemp. Math., 8, Amer. Math. Soc., Providence, 1982, pp. 289-295.10.1090/conm/008/653187
DOI: https://doi.org/10.1515/amsil-2017-0017 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
Language: English
Page range: 99 - 131
Submitted on: Sep 8, 2016
Accepted on: Dec 31, 2017
Published on: Aug 24, 2018
Published by: University of Silesia in Katowice, Institute of Mathematics
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2018 Ron Brown, Jonathan L. Merzel, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.