Proof of the Inner Automorphism Theorem for Endomorphism Algebras

[losiu99]

I have encountered a statement: Every automorphism of an algebra of endomorphisms of a vector space is an inner automorphism. I tried to prove it, but so far I fail. Does anyone know where can I find a proof of this theorem (it was stated as "well-known"), or provide a sketch?
Thank you very much in advance!

 

[arkajad]

Perhaps http://books.google.fr/books?id=MDU...page&q=skolem noether "vector space"&f=false" - p. 154, Corollary 2.

 

[losiu99]

Thank you, pdf on semisimple algebras seems to contain what I was looking for. Once again, thanks for quick and accurate help!