A quadratic analogue of Serre's theorem on projective modules (Q1094470)

Let R be a commutative Noetherian ring, A be an R-algebra with involution, (M,[f]) be a quadratic space over A, where M is a finitely generated projective right A-module, f is a non-singular sesquilinear form \(M\times M\to A\) [\textit{H. Bass}, Algebraic K-theory. III, Proc. Conf. Battelle Inst. 1972, Lect. Notes Math. 343, 57-265 (1973; Zbl 0299.18005)]. The existence of an orthogonal summand for (M,[f]) is deduced (under some assumptions) from this property for any \((M_{{\mathfrak M}},[f_{{\mathfrak M}}])\) where \({\mathfrak M}\) is a maximal ideal of R.