On trace forms and the Burnside ring

The Tambara Structure of the Trace Ideal for Cyclic Extensions

“…Proof. A theorem of Epkenhans says that the absolute trace ideal is an intersection of finitely many trace ideals [6]. This, along with our computations of the trace ideal and Epkenhans computation of T (G/G) imply the desired result.…”

“…We will refer to this object as the absolute trace ideal to avoid confusion, although previous literature does not include the descriptive. Epkenhans[5,6] determines the absolute trace ideal of elementary Abelian 2-groups, cyclic 2-groups, and the quaternion and dihedral groups of order 8.…”

On the annihilating ideal for trace forms

“…Hence mi == 0 mod 4. We conclude (2,X) C (IM(G,H) : (SignM~G,H)~X)))~ By the preceeding theorem and by proposition 5.5 in [8] IM(G,H)S ince (2, X) is a maximal ideal in Z[X], we are done. [3] corollary 1.6.5, resp.…”

“…Let Qn be the class of all quadratic forms of dimension n. Then 7~~ is a principal ideal generated by the f (X) with L -K[X]/(f(X)) (see [13] [5] (see also [7, proposition 3] [6], [7], [8] [8]. By proposition 3, theorem 6 and [6, proposition 7] we get 2(X -n)(X -s) E IMG, H .…”