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Suppose D is a Dedekind domain of characteristic 2 and ( M. <2) (F(2)) to denote the subring of D (F) of all squares. If (M, <p) and (FM, (p) are inner product spaces, then ?2(M) = (<p(m, m)|/neM) and â(FM) = {<p(x, x)|xe FM} are subgroups of D and F, respectively. They become D(2) or F(2) sub modules when we define a2 ■ <p(m, m) = <p(am, am) for a in D or F, or they become D or F submodules when we define a ° <p(m, m) = cp(am, am). 3.(M) and £(FM) are called the value modules of the respective inner product spaces. We note that qp: M -* â(M), defined by qv(m) = <p(m, m), is a D module homomorphism when3.1 M) is viewed as a D module. If P is a projective module over an arbitrary commutative ring and k is an arbitrary symmetric bilinear form on P, we let P* = rIomn(f, D) and define the

On inner product spaces over Dedekind domains of characteristic two