The ramification is tame when the ramification indices \(e_{i}\) are all relatively prime to the residue characteristic \(p\) of \(p\), otherwise wild. A finite generically etale extension \(B / A\) of Dedekind domains is tame if and only if the trace \(\operatorname{Tr}: B \rightarrow A\) is surjective. # Results

Can define trace and norm of \(x\) as the trace and determinant of the map \(m_x: a\mapsto ax\).

See also transfer, norm.