Linear algebra, field morphisms and linear independence

  • #1
1
0

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.
 

Answers and Replies

  • #2
15,564
13,677

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.
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\,.##
 

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