Structure of the center of a Clifford algebra over an integral domain (Q800989)

Let R be an integral domain of characteristic different from 2, M a free R-module with a finite basis \(e_ 1,...,e_ n\) and \(f: M\times M\to R\) a symmetric bilinear form with \(\det (f_{ij})\neq 0\), where \(f_{ij}=f(e_ i,e_ j)\) and \(i,j=1,...,n\). The author shows that the center of the Clifford algebra C of the pair (M,f) equals \(R^*1_ C\) if n is even, and \(R^*1_ C\oplus R^*e\) if n is odd. Here \(1_ C\) is the identity element of C and e a certain element described explicitly.