Automorphisms and subalgebras of free algebras

P. Cohn proved that free associative algebras are free ideal rings (FI-ring or fir), i.e., 
every submodule of a free module over a free associative algebra is free.  This result easily
implies that subalgebras of free Lie algebras are free and automorphisms of finitely generated free Lie algebras are tame. 

Let $P(x_1,...,x_n)$ be a free Poisson field, i.e., the quotient field of a free Poisson algebra
with extended Poisson bracket. In a joint work with L. Makar-Limanov we proved that
(a) the universal enveloping algebra $P(x_1,...,x_n)^e$ of $P(x_1,...,x_n)$ is a free ideal
ring; and (b) the automorphism group of a free Poisson field in two variables is isomorphic
to the two dimentional Cremona group. 

I will talk on these results and give some survey of results about tame and wild automorphisms
of polynomial and free associative algebras.