Embedding Witt rings of Dedekind domains

Abstract

Let W( R) denote Harrison's Witt ring of the commutative ring R. In case R is a field of characteristic ≠ 2, this is the classical Witt ring based on anisotropic quadratic forms. In this note we determine under what conditions W( R) is embedded in W( S) for certain Dedekind domains R ⊂ S. In particular, an answer is given in case R and S are the integers in algebraic number fields K and L, respectively, with ( L: K) odd.