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On the Computation of Integral Closures of Cyclic Extensions of Function Fields
Published online by Cambridge University Press: 01 February 2010
Abstract
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Let S be a non-empty proper subset of the set of places of a global function field F and E a cyclic Kummer or Artin–Schreier–Witt extension of F. We present a method of efficiently computing the ring of elements of E which are integral at all places of S. As an important tool, we include an algorithmic version of the strong approximation theorem. We conclude with several examples.
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- Copyright © London Mathematical Society 2007
References
1.Buhler, J. P., Lenstra, H. W., Jr and Pomerance, Carl, ‘Factoring integers with the number field sieve’, The development of the number field sieve, Lecture Notes in Math. 1554 (Springer, Berlin, 1993) 50–94.CrossRefGoogle Scholar
2.Cannon, J. et al. , The computer algebra system MAGMA (University of Syd ney, 2004), http://magma.maths.usyd.edu.au/magma/.Google Scholar
3.Cassels, J.W.S., Local fields, London Mathematical Society Student Texts 3 (Cambridge University Press, Cambridge, 1986).Google Scholar
4.Fraatz, R., ‘Computation of maximal orders of cyclic extensions of function fields’, thesis, Technische Universität Berlin, (2005), http://www.math.tu-berlin.de/~kant/publications/diss/diss_Robert-Fraatz.pdf.Google Scholar
5.Friedrichs, C., ‘Bestimmung relativer Ganzheitsbasen mit dem Round-2-Algorithmus’, Diplomarbeit, Technische Universität Berlin, (1997), http://www.math.tu-berlin.de/~kant/publications/diplom/friedrichs.ps.gzGoogle Scholar
6.Friedrichs, C., ‘Berechnung von Maximalordnungen über Dedekindringen’, thesis, Technische Universität Berlin, (2000), http://www.math.tu-berlin.de/~kant/publications/diss/diss_fried.pdfGoogle Scholar
7.Goppa, V. D., ‘Codes on algebraic curves’, ,Dokl. Akad. Nauk SSSR 259 (1981) 1289–1290.Google Scholar
8.Goppa, V. D., Geometry and codes, Mathematics and its Applications (Soviet Series) 24 (Kluwer, Dordrecht, 1988).Google Scholar
9.Hasse, H., ‘Theorie der relativ-zyklischen algebraischen Funktionenkörper, insbesondere bei endlichem Konstantenkörper’, J. Reine Angew. Math. 172 (1934) 37–54.Google Scholar
10.Hess, F., ‘Computing Riemann-Roch spaces in algebraic function fields and related topics’, J. Symbolic Comput. 33 (2002) 425–445.CrossRefGoogle Scholar
11.Lorenz, F., Einführung in die Algebra. Teil II (Bibliographisches Institut, Mannheim, 1990).Google Scholar
12.Pohst, M. and Zassenhaus, H., Algorithmic algebraic number theory, Encyclopedia of Mathematics and its Applications 30 (Cambridge University Press, Cambridge, 1997).Google Scholar
13.Schmid, H. L., ‘Zyklische algebraische Funktionenkörper vom Grade pn über endlichem Konstantenkörper der Charakteristik p’ J. Reine Angew. Math. 175 (1936) 108–123.CrossRefGoogle Scholar
14.Stichtenoth, H., Algebraic function fields and codes, Universitext (Springer, Berlin, 1993).Google Scholar
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