On the annihilating ideal for trace forms

Martin Epkenhans

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 1, page 115-124
  • ISSN: 1246-7405

Abstract

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We give several examples of classes of trace forms for which the ideal of annihilating polynomials is principal. We prove, that in general, the annihilating ideal is not a principal ideal.

How to cite

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Epkenhans, Martin. "On the annihilating ideal for trace forms." Journal de théorie des nombres de Bordeaux 15.1 (2003): 115-124. <http://eudml.org/doc/249084>.

@article{Epkenhans2003,
abstract = {We give several examples of classes of trace forms for which the ideal of annihilating polynomials is principal. We prove, that in general, the annihilating ideal is not a principal ideal.},
author = {Epkenhans, Martin},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {trace forms; annihilating ideals},
language = {eng},
number = {1},
pages = {115-124},
publisher = {Université Bordeaux I},
title = {On the annihilating ideal for trace forms},
url = {http://eudml.org/doc/249084},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Epkenhans, Martin
TI - On the annihilating ideal for trace forms
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 115
EP - 124
AB - We give several examples of classes of trace forms for which the ideal of annihilating polynomials is principal. We prove, that in general, the annihilating ideal is not a principal ideal.
LA - eng
KW - trace forms; annihilating ideals
UR - http://eudml.org/doc/249084
ER -

References

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  1. [1] P. Beaulieu, T. Palfrey, The Galois number. Math. Ann.309 (1997), 81-96. Zbl0885.11027MR1467647
  2. [2] P.E. Conner, A proof of the conjecture concerning algebraic Witt classes. unpublished, 1987. 
  3. [3] P.E. Conner, R. Perlis, A survey of trace forms of algebraic number fields. World Scientific, Singapore, 1984. Zbl0551.10017MR761569
  4. [4] C.W. Curtis, I. Reiner, Methods of representation theory, volume II. John Wiley and Sons, New York, 1987. Zbl0616.20001MR892316
  5. [5] A.W.M. Dress, Notes on the theory of representations of finite groups. Unpublished notes, 1971. 
  6. [6] M. Epkenhans, On vanishing theorems for trace forms. Acta Math. Inform. Univ. Ostraviensis6 (1998), 69-85. Zbl1024.11021MR1822517
  7. [7] M. Epkenhans, An analogue of Pfister's local-global principle in the Burnside ring. J. Théor. Nombres Bordeaux11 (1999), 31-44. Zbl0964.11021MR1730431
  8. [8] M. Epkenhans, On trace forms and the Burnside ring. In Quadratic forms and their applications, ed. by Eva Bayer-Fluckiger, David Lewis and Andrew Ranicki. Contemporary Math., volume 272, pages 39-56, AMS, Providence, RI, 2000. Zbl0987.11025MR1803360
  9. [9] M. Epkenhans, O. Gerstengarbe, On the Galois number and minimal degree of doubly transitive groups. Comm. Algebra28 (2000), 4889-4900. Zbl0985.20001MR1779881
  10. [10] B. Huppert, Endliche Gruppen I. Die Grundlagen der mathematischen Wissenschaften. Springer-Verlag, Berlin, Heidelberg, New York, 1967. Zbl0217.07201MR224703
  11. [11] D.W. Lewis, Witt rings as integral rings. Invent. Math.90 (1987), 631-633. Zbl0629.10017MR914852
  12. [12] D.W. Lewis, S. Mcgarraghy, Annihilating polynomials, étale algebras, trace forms and the Galois number. Arch. Math.75 (2000), 116-120. Zbl0957.11021MR1767167
  13. [13] O. Taussky, The discriminant matrices of an algebraic number field. J. London Math. Soc.43 (1968), 152-154. Zbl0155.37903MR228473
  14. [14] A.D. Thomas, G.V. Wood, Group tables. Shiva Publishing Limited, 1980. Zbl0441.20001

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