I'm working through a proof which is rather algebraic, and my abstract algebra is probably only basic to intermediate. I have a differential extension $E/K$ of a differential field $K$, and the proof applies the trace map $Tr$ to both sides of an equation.
I can not find a definition of the trace map in the book, and I think it may be (elementary?) assumed knowledge. What are the definitions of the trace (and norm) maps? I'm guessing it's some kind of morphism? (by which I mean a map with certain properties)