Originally Posted by

**Swlabr** Essentially, I believe my question boils down to this: does the correspondence theorem at least partially hold for Lie algebras (or, indeed, any algebra)?

$\displaystyle K, L$ Lie algebras, $\displaystyle K \leq L$. Let $\displaystyle \phi$ be some homomorphism of Lie algebras and let $\displaystyle K\phi$ be an ideal of $\displaystyle L\phi$, $\displaystyle K\phi \unlhd L\phi$. Then is it true that $\displaystyle K \unlhd L$?

This seems to be used in a proof in my lecture notes, but I can't work out why it holds (if, indeed, it does)!

Thanks in advance.