Manis valuations and Prüfer extensions

 Access to full text

 Full (PDF)

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