Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 7, Pages 1141-1147
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.