International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 7, Pages 1141-1147
doi:10.1155/IJMMS.2005.1141
Witt group of Hermitian forms over a noncommutative
discrete valuation ring
Département de Mathématiques, Faculté des Sciences et Techniques, Université Moulay Ismaïl, B. P. 509 Boutalamine, Errachidia 52 000, Morocco
Received 16 June 2004; Revised 28 February 2005
Copyright © 2005 L. Oukhtite. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We investigate Hermitian forms on finitely generated
torsion modules over a noncommutative discrete valuation ring.
We also give some results for lattices, which still are satisfied
even if the base ring is not commutative. Moreover, for a
noncommutative discrete-valued division algebraD with
valuation ring R and residual division algebra D¯, we prove
that W(D¯)≅WT(R), where WT(R) denotes the Witt group
of regular Hermitian forms on finitely generated torsion R-modules.