Abstract
In this note we give algebraic characterizations of the concepts genus and rational equivalence class for integral norm forms. Combining this with a result of Komatsu, we obtain many examples of two integral forms belonging to the same genus (i.e., forms which are equivalent over every p-adic completion 7Zp, including the real numbers Z~o ) but which are not rationally equivalent. Let {Oi} and {~/j} be bases for two algebraic number fields K and L of degrees n and m over ~. We assume the 0 i and t/j to be algebraic integers. Then the norm forms
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