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Annihilating polynomials for quadratic forms and Stirling numbers of the second kind
Author(s) -
De Wannemacker Stefan
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410551
Subject(s) - mathematics , annihilator , conjecture , quadratic equation , ideal (ethics) , pure mathematics , ring (chemistry) , maximal ideal , torsion (gastropod) , discrete mathematics , algebra over a field , geometry , law , chemistry , medicine , surgery , organic chemistry , political science
We 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. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)