Witt group of Hermitian forms over a noncommutative discrete valuation ring

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.