Manis valuations and Prüfer extensions

Manfred Knebusch

Banach Center Publications (1998)

  • Volume: 44, Issue: 1, page 141-146
  • ISSN: 0137-6934

How to cite


Knebusch, Manfred. "Manis valuations and Prüfer extensions." Banach Center Publications 44.1 (1998): 141-146. <>.

author = {Knebusch, Manfred},
journal = {Banach Center Publications},
keywords = {Manis valuation; real spectrum; real semi-algebraic geometry; Prüfer extensions},
language = {eng},
number = {1},
pages = {141-146},
title = {Manis valuations and Prüfer extensions},
url = {},
volume = {44},
year = {1998},

AU - Knebusch, Manfred
TI - Manis valuations and Prüfer extensions
JO - Banach Center Publications
PY - 1998
VL - 44
IS - 1
SP - 141
EP - 146
LA - eng
KW - Manis valuation; real spectrum; real semi-algebraic geometry; Prüfer extensions
UR -
ER -


  1. [A] T. Akiba, Remarks on generalized rings of quotients, III, J. Math. Kyoto Univ. 9 (1969), 205-212. Zbl0187.00402
  2. [B] E. Becker, Valuations and real places in the theory of formally real fields, in: Géométrie algébrique réelle et formes quadratiques, J.-L. Colliot-Théléne et al. (ed.), Lecture Notes in Math. 959, Springer, Berlin-New York, 1982, 1-40. 
  3. [B1] E. Becker, On the real spectrum of a ring and its applications to semialgebraic geometry, Bull. Amer. Math. Soc. (N.S.) 15 (1986), 19-60. Zbl0634.14016
  4. [B2] E. Becker, Partial orders on a field and valuation rings, Comm. Algebra 7 (1979), 1933-1976. Zbl0432.12011
  5. [B3] E. Becker, Theory of Real Fields and Sums of Powers, forthcoming book. 
  6. [BP] E. Becker and V. Powers, Sums of powers in rings and the real holomorphy ring, J. Reine Angew. Math. 480 (1996), 71-103. Zbl0922.12003
  7. [Be] R. Berr, Basic principles for a morphological theory of semi-algebraic morphisms, Habilitationsschrift, Univ. Dortmund, 1994. 
  8. [BCR] J. Bochnak, M. Coste, M.-F. Roy, Géométrie algébrique réelle, Ergeb. Math. Grenzgeb. (3) 12, Springer, Berlin, 1987. Zbl0633.14016
  9. [Bo] N. Bourbaki, Algèbre commutative, Chap. 1-7, Hermann, Paris, 1961-1965. 
  10. [BS] L. Bröcker, J.-H. Schinke, On the L-adic Spectrum, Schriftenreihe Math. Inst. Univ. Münster 2. Ser. 40, Münster, 1986. 
  11. [D] A. Dress, Lotschnittebenen mit halbierbarem rechten Winkel, Arch. Math. (Basel) 16 (1965), 388-392. Zbl0137.40204
  12. [Gi] R. Gilmer, Two constructions of Prüfer domains, J. Reine Angew. Math. 239/240 (1970), 153-162. Zbl0184.29102
  13. [Gr] J. Gräter, Der allgemeine Approximationssatz für Manisbewertungen, Monatsh. Math. 93 (1982), 277-288. Zbl0481.13001
  14. [G1] M. Griffin, Prüfer rings with zero divisors, J. Reine Angew. Math. 239/240 (1970), 55-67. Zbl0185.09801
  15. [G2] M. Griffin, Valuations and Prüfer rings, Canad. J. Math. 26 (1974), 412-429. Zbl0259.13008
  16. [Huc] J. A. Huckaba, Commutative Rings with Zero Divisors, Marcel Dekker, New York, 1988. Zbl0637.13001
  17. [Kn] M. Knebusch, On valuation spectra, this volume. 
  18. [KS] M. Knebusch and C. Scheiderer, Einführung in die reelle Algebra, Vieweg, Braunschweig, 1989. Zbl0732.12001
  19. [KZ] M. Knebusch and Digen Zhang, Manis valuations and Prüfer extensions I, Doc. Math. 1 (1996), 149-197. Zbl0855.13001
  20. [Ko] S. Kochen, Integer valued rational functions over the p-adic numbers: A p-adic analogue of the theory of real fields, in: Number Theory, Proc. Symp. Pure Math. XII, 57-73, Amer. Math. Soc., Providence, 1969. 
  21. [La] T. Y. Lam, Orderings, Valuations and Quadratic Forms, CBMS Regional Conference Series in Math. 52, Amer. Math. Soc., Providence, 1983. 
  22. [LM] M. Larsen and P. McCarthy, Multiplicative Theory of Ideals, Academic Press, New York-London, 1971. 
  23. [L] D. Lazard, Autour de la platitude, Bull. Soc. Math. France 97 (1969), 81-128. Zbl0174.33301
  24. [M] M. E. Manis, Valuations on a commutative ring, Proc. Amer. Math. Soc. 20 (1969), 193-198. Zbl0179.34201
  25. [Mar] M. Marshall, Orderings and real places on commutative rings, J. Algebra 140 (1991), 484-501. Zbl0752.13002
  26. [P] V. Powers, Valuations and higher level orders in commutative rings, J. Algebra 172 (1995), 255-272. Zbl0845.11016
  27. [Pt] M. Prechtel, Universelle Vervollständigungen in der Kategorie der reell abgeschlossenen Räume, Dissertation, Univ. Regensburg, 1992. 
  28. [PR] A. Prestel and P. Roquette, Formally p-adic Fields, Lecture Notes in Math. 1050, Springer, Berlin-New York, 1984. Zbl0523.12016
  29. [Rh] C. P. L. Rhodes, Relative Prüfer pairs of commutative rings, Comm. Algebra 19 (1991), 3423-3445. Zbl0747.13013
  30. [R] P. Roquette, Bemerkungen zur Theorie der formal p-adischen Körper, Beiträge Algebra Geom. 1 (1971), 177-193. Zbl0245.12101
  31. [Sa] P. Samuel, La notion de place dans un anneau, Bull. Soc. Math. France 85 (1957), 123-133. Zbl0079.05502
  32. [S] H.-W. Schülting, Real holomorphy rings in real algebraic geometry, in: Géométrie algébrique réelle et formes quadratiques, J.-L. Colliot-Théléne et al. (ed.), Lecture Notes in Math. 959, Springer, Berlin-New York, 1982, 433-442. 
  33. [Sch] N. Schwartz, The Basic Theory of Real Closed Spaces, Regensburger Math. Schriften 15, Regensburg, 1987. 
  34. [Sch1] N. Schwartz, The Basic Theory of Real Closed Spaces, Mem. Amer. Math. Soc. 397 (1989). Zbl0697.14015

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.