Embedding Henselian fields into power series

Journal of Algebra

Volumn 304, Issue 1, 2006, Pages 112-156

  Fornasiero, Antongiulio ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Henselian field; Integer part; Valuation

Indexed keywords

EID: 33747773015     PISSN: 00218693     EISSN: 1090266X     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2006.06.037     Document Type: Article

References (30)

1. α. Trans. Amer. Math. Soc. 103 3 (1962) 341-352
2. Association of Symbolic Logic. In: Enayat A., Kalantari I., and Moniri M. (Eds). Logic in Tehran, Proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic. Tehran, Iran, 2003. Lect. Notes Log. vol. 26 (2006), AK Peters, Ltd.
3. Ax J. A Metamathematical Approach to Some Problems in Number Theory. Proc. Sympos. Pure Math. vol. 20 (1969), Amer. Math. Soc.
4. Ax J., and Kochen S. Diophantine problems over local fields I, II. Amer. J. Math. 87 (1965) 605-648
5. Ax J., and Kochen S. Diophantine problems over local fields III. Decidable fields, Ann. of Math. (2) 83 (1966) 437-456
6. Biljakovic D., Kochetov M., and Kuhlmann S. Primes and irreducibles in truncation integer parts of real closed fields. Proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic [2] (2006)
7. Boughattas S. Optimal results on the existence of an integer part in ordered fields. J. Symbolic Logic 58 1 (1993) 326-333
8. Conway J.H. On Numbers and Games. London Math. Soc. Monogr. vol. 6 (1976), Academic Press [Harcourt Brace Jovanovich Publishers], London
9. F. Delon, Quelques propriétés des corps valués en théories des modèles, PhD thesis, Paris VII, 1981
10. van den Dries L., and Ehrlich P. Erratum to: Fields of surreal numbers and exponentiation. Fund. Math. 168 3 (2001) 295-297
11. Ehrlich P. Number systems with simplicity hierarchies: A generalization of Conway's theory of surreal numbers. J. Symbolic Logic 66 3 (2001) 1231-1258
12. Ershov Y.L. On the elementary theory of maximal normed fields. Dokl. Akad. Nauk SSSR 165 (1965) 21-23 English translation:
13. Ershov Y.L. On the elementary theory of maximal normed fields. Sov. Math. Dokl. 6 (1965) 1390-1393
14. A. Fornasiero, Integration on surreal numbers, PhD thesis, University of Edinburgh, January 2004
15. Greenberg M.J. Lectures on Forms in Many Variables (1969), Benjamin, New York
16. Kaplansky I. Maximal fields with valuations I. Duke Math. J. 9 (1942) 303-321
17. Kaplansky I. Selected Papers and Other Writings (1995), Springer-Verlag, New York (with an introduction by Hyman Bass)
18. Kochen S. The model theory of local fields. Logic Conference Kiel. Lecture Notes in Math. vol. 499 (1975) 384-425
19. Kuhlmann F.-V. Additive polynomials and their role in the model theory of valued fields. Proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic [2] (2006)
20. Kuhlmann F.-V. Dense subfields of Henselian fields, and integer parts. Proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic [2] (2006)
21. Kuhlmann F.-V. Value groups, residue fields, and bad places of rational function fields. Trans. Amer. Math. Soc. 356 11 (2004) 4559-4600
22. Kuhlmann F.-V., and Prestel A. On places of algebraic function fields. J. Reine Angew. Math. 353 (1984) 181-195
23. Mourgues M.H., and Ressayre J.-P. Every real closed field has an integer part. J. Symbolic Logic 58 2 (1993) 641-647
24. Prestel A., and Delzell C.N. Positive Polynomials. Springer Monogr. Math. (2001), Springer-Verlag, Berlin
25. Prestel A., and Roquette P. Formally p-Adic Fields. Lecture Notes in Math. vol. 1050 (1984), Springer-Verlag, Berlin
26. Rayner F.J. An algebraically closed field. Glasgow Math. J. 9 (1968) 146-151
27. Ribenboim P. Equivalent forms of Hensel's lemma. Expo. Math. 3 1 (1985) 3-24
28. Ribenboim P. Thèorie des valuations. second ed. (1968), Les Presses de l'Universitè de Montrèal, Montrèal
29. Schilling O.F.G. The Theory of Valuations. Math. Surveys Monogr. (1950), Amer. Math. Soc., Providence, RI
30. Whaples G. Galois cohomology of additive polynomials and nth power mappings of fields. Duke Math. J. 24 (1957) 143-150