2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124744We present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non-vanishing condition on the powers of the fundamental ideal in the torsion part of the Witt ring. This settles a conjecture of Ongenae and Van Geel. This result could only be proved by first obtaining a new lower bound on the 2-adic valuation of Stirling numbers of the second kind.13 pages, accepted by Mathematische NachrichtenNumber TheoryRings and Algebrastext