Infinite towers of Galois defect extensions of Kaplansky fields

Anna Blaszczok

Published: 2018-01-31

Vol. 32 (2018)

Infinite towers of Galois defect extensions of Kaplansky fields

Anna Blaszczok

Abstract

We give conditions for Kaplansky fields to admit infinite towers of Galois defect extensions of prime degree. As proofs of the presented facts are constructive, this provides examples of constructions of infinite towers of Galois defect extensions of prime degree. We also give a constructive proof of the fact that a henselian Kaplansky field cannot be defectless-by-finite.

Keywords:

defect extensions , Kaplansky fields , Artin–Schreier defect extensions , Kummer defect extensions , defectless-by-finite fields

Download files

PDF

Citation rules

Blaszczok, A. (2018). Infinite towers of Galois defect extensions of Kaplansky fields. Annales Mathematicae Silesianae, 32, 65–78. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13913

Similar Articles

Mohamed Akkouchi, Well-posedness of the fixed point problem for certain asymptotically regular mappings , Annales Mathematicae Silesianae: Vol. 23 (2009)
Paweł Gładki, Orderings of higher level in multifields and multirings , Annales Mathematicae Silesianae: Vol. 24 (2010)
Mieczysław Kula, Małgorzata Serwecińska, Communication complexity and linearly ordered sets , Annales Mathematicae Silesianae: Vol. 29 (2015)
Jens Schwaiger, Functional equations for homogeneous polynomials arising from multilinear mappings and their stability , Annales Mathematicae Silesianae: Vol. 8 (1994)
Maciej Sablik, Differentiable solutions of functional equations in Banach spaces , Annales Mathematicae Silesianae: Vol. 7 (1993)
Alfred Czogała, Beata Rothkegel, Andrzej Sładek, Wild primes of a higher degree self-equivalence of a number field , Annales Mathematicae Silesianae: Vol. 30 (2016)
Hans Buchmann, Examples of convolution products , Annales Mathematicae Silesianae: Vol. 2 (1986)

<< < 1 2 3 4 5 6

You may also start an advanced similarity search for this article.

References

1. Blaszczok A., Infinite towers of Artin–Schreier defect extensions of rational function fields, in: A. Campillo, F.-V. Kuhlmann, B. Teissier (Eds.), Valuation theory in interaction, EMS Series of Congress Reports, European Mathematical Society (EMS), Zürich, 2014, pp. 16–54.
2. Blaszczok A., Distances of elements in valued field extensions, submitted.
3. Blaszczok, A., Kuhlmann F.-V., Algebraic independence of elements in immediate extensions of valued fields, J. Algebra 425 (2015), 179–214.
4. Blaszczok A., Kuhlmann F.-V., On maximal immediate extensions of valued fields, Math. Nachr. 290 (2017), 7–18.
5. Endler O., Valuation theory, Springer-Verlag, Berlin, 1972.
6. Kaplansky I., Maximal fields with valuations, Duke Math. J. 9 (1942), 303–321.
7. Karpilovsky G., Topics in field theory, North-Holland Mathematics Studies 155, North-Holland Publishing Co., Amsterdam, 1989.
8. Krull W., Allgemeine Bewertungstheorie, J. Reine Angew. Math. 167 (1932), 160–196.
9. Kuhlmann F.-V., Henselian function fields and tame fields, preprint (extended version of Ph.D. thesis), Heidelberg, 1990.
10. Kuhlmann F.-V., Valuation theoretic and model theoretic aspects of local uniformization, in: H. Hauser, J. Lipman, F. Oort, A. Quirós (Eds.), Resolution of singularities. A research textbook in tribute to Oscar Zariski, Progress in Mathematics 181, Birkhäuser Verlag, Basel, 2000, pp. 381–456.
11. Kuhlmann F.-V., Value groups, residue fields, and bad places of rational function fields, Trans. Amer. Math. Soc. 356 (2004), 4559–4600.
12. Kuhlmann F.-V., A classification of Artin–Schreier defect extensions and characterizations of defectless fields, Illinois J. Math. 54 (2010), 397–448.
13. Kuhlmann F.-V., The defect, in: M. Fontana, S.-E. Kabbaj, B. Olberding, I. Swanson (Eds.), Commutative algebra. Noetherian and non-Noetherian perspectives, Springer-Verlag, New York, 2011, pp. 277–318.
14. Kuhlmann F.-V., The algebra and model theory of tame valued fields, J. Reine Angew. Math. 719 (2016), 1–43.
15. Kuhlmann F.-V., Elimination of ramification II: henselian rationality of valued function fields, in preparation.
16. Whaples G., Galois cohomology of additive polynomial and n-th power mappings of fields, Duke Math. J. 24 (1957), 143–150. Google Scholar

Vol. 32 (2018)
Published: 2018-08-24

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

Submit