Definition galTrace U V a := \sum_(x in 'Gal(V / U)) (x a).
Definition galNorm U V a := \prod_(x in 'Gal(V / U)) (x a).
Section TraceAndNormMorphism.
Variables U V : {vspace L}.
Fact galTrace_is_additive : additive (galTrace U V).
Canonical galTrace_additive := Additive galTrace_is_additive.

Lemma galNormX n : {morph galNorm U V : a / a ^+ n}.