A remark on quadratic spaces over noncommutative semilocal rings (Q1107563)

Witt's Cancellation Theorem for quadratic spaces over noncommutative semilocal rings does not hold in general. A ring \(A\) of \(2\times 2\)-matrices and a projective \(A\)-module \(P\) with two nonisomorphic quadratic space structures \(g\) and \(h\) are constructed such that \((P,g)\bot {\mathcal H}(A)\cong (P,h)\bot {\mathcal H}(A)\) (\({\mathcal H}(A)\) the hyperbolic plane). Given the quadratic space \(P\) an upper bound for the number of isometry classes of spaces \(N\) with \(P\bot {\mathcal H}(A)\cong N\bot {\mathcal H}(A)\) is determined.