simple extension

[Al Don Gate]

Hi,

 

Let $L/K$ be a simple extension : $L/K$ is a a field extension and it exits $x\in L$ such that L=K(x).

 

I consider the endomorphism of L $m_x$ define by $m_x(y)=xy$.

 

My problem :

 

I find ( and i can explain if somebody want...) that the characteristic polynomial of m_x is 0 !!! It involves that the degree of the extension is 0??? How is it possible?