Abstract
We investigate the relationship between the determinants det (P) and norms N ( P ) of right modules P of rank one over associative composition algebras C. We show: \( {\rm det} (P) \cong N(P) \otimes N(P) \) if C is a quaternion algebra, and \( {\rm det}\,(P) \cong N(P) \otimes {\rm det}\, (C)\) if C is a quadratic etale algebra.
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