On the annihilating ideal for trace forms
Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 115-124.

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.

Nous donnons plusieurs exemples de familles de formes trace dont l’idéal annulateur dans [𝕏] est principal. Nous montrons aussi qu’en général, cet idéal n’est pas principal.

@article{JTNB_2003__15_1_115_0,
     author = {Epkenhans, Martin},
     title = {On the annihilating ideal for trace forms},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {115--124},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     mrnumber = {2019004},
     zbl = {1048.11027},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_2003__15_1_115_0/}
}
TY  - JOUR
AU  - Epkenhans, Martin
TI  - On the annihilating ideal for trace forms
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2003
SP  - 115
EP  - 124
VL  - 15
IS  - 1
PB  - Université Bordeaux I
UR  - http://archive.numdam.org/item/JTNB_2003__15_1_115_0/
LA  - en
ID  - JTNB_2003__15_1_115_0
ER  - 
%0 Journal Article
%A Epkenhans, Martin
%T On the annihilating ideal for trace forms
%J Journal de théorie des nombres de Bordeaux
%D 2003
%P 115-124
%V 15
%N 1
%I Université Bordeaux I
%U http://archive.numdam.org/item/JTNB_2003__15_1_115_0/
%G en
%F JTNB_2003__15_1_115_0
Epkenhans, Martin. On the annihilating ideal for trace forms. Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 115-124. http://archive.numdam.org/item/JTNB_2003__15_1_115_0/

[1] P. Beaulieu, T. Palfrey, The Galois number. Math. Ann. 309 (1997), 81-96. | MR | Zbl

[2] P.E. Conner, A proof of the conjecture concerning algebraic Witt classes. unpublished, 1987.

[3] P.E. Conner, R. Perlis, A survey of trace forms of algebraic number fields. World Scientific, Singapore, 1984. | MR | Zbl

[4] C.W. Curtis, I. Reiner, Methods of representation theory, volume II. John Wiley and Sons, New York, 1987. | MR | Zbl

[5] A.W.M. Dress, Notes on the theory of representations of finite groups. Unpublished notes, 1971.

[6] M. Epkenhans, On vanishing theorems for trace forms. Acta Math. Inform. Univ. Ostraviensis 6 (1998), 69-85. | MR | Zbl

[7] M. Epkenhans, An analogue of Pfister's local-global principle in the Burnside ring. J. Théor. Nombres Bordeaux 11 (1999), 31-44. | Numdam | MR | Zbl

[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. | MR | Zbl

[9] M. Epkenhans, O. Gerstengarbe, On the Galois number and minimal degree of doubly transitive groups. Comm. Algebra 28 (2000), 4889-4900. | MR | Zbl

[10] B. Huppert, Endliche Gruppen I. Die Grundlagen der mathematischen Wissenschaften. Springer-Verlag, Berlin, Heidelberg, New York, 1967. | MR | Zbl

[11] D.W. Lewis, Witt rings as integral rings. Invent. Math. 90 (1987), 631-633. | MR | Zbl

[12] D.W. Lewis, S. Mcgarraghy, Annihilating polynomials, étale algebras, trace forms and the Galois number. Arch. Math. 75 (2000), 116-120. | MR | Zbl

[13] O. Taussky, The discriminant matrices of an algebraic number field. J. London Math. Soc. 43 (1968), 152-154. | MR | Zbl

[14] A.D. Thomas, G.V. Wood, Group tables. Shiva Publishing Limited, 1980. | Zbl