The field trace 
in a finite extension 
is the matrix trace of the
-linear
transformation 
on 
. For a separable
extension, it equals the sum of the images of 
under the field embeddings
of 
into an algebraic
closure of 
.
For example, 
(Milne 2020).
Field Trace
See also
Field Norm, Finite Extension, Matrix Trace, Number Field DiscriminantExplore with Wolfram|Alpha
References
Milne, J. S. "Algebraic Number Theory." 19 Jul 2020. https://www.jmilne.org/math/CourseNotes/ANT.pdf.Cite this as:
Weisstein, Eric W. "Field Trace." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FieldTrace.html