Field norm
In mathematics, the (field) norm is a particular mapping defined in field theory, which maps elements of a larger field into a subfield. == Formal definition == Let K be a field and L a finite extension (and hence an algebraic extension) of K. The field L is then a finite-dimensional vector space over K. Multiplication by α, an element of L, m α : L → L {\displaystyle m_{\alpha }\colon L\to L} m α ( x ) = α x {\displaystyle m_{\alpha }(x)=\alpha x} , is a K-linear transformation of this vector space into itself.