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

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

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.

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Epkenhans, Martin. On the annihilating ideal for trace forms. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 115-124. http://www.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 unpublished, 1987.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 Unpublished notes, 1971.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