The discussion focuses on proving the linear independence of field morphisms f1, f2, ..., fn from field K to field L, under the condition that fi != fj for all i ≠ j. It is established that since each fi is a field morphism, the kernel of each morphism is zero, confirming their injectivity. The approach suggested involves starting with small values of n (specifically n=1 and n=2) to build a foundation for a general proof or to apply mathematical induction.
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In such cases it is often helpful to start with ##n=1## and ##n=2## to see how possible arguments work. From there one can either proceed by a general ##n## or per induction. I assume we also have to require ##f_i \neq 0\,.##mariang said:Homework Statement
Let f1,f2, ..., fn : K -> L be field morphisms. We know that fi != fj when i != j, for any i and j = {1,...,n}. Prove that f1,f2, ..., fn are linear independent / K.
Homework Equations
f1, ..., fn are field morphisms => Ker (fi) = 0 (injective)
The Attempt at a Solution
I tried to use the linearity and the injectivity but i got stuck.