Abstract
Let
S and
R be the rings of regular functions on affine algebraic varieties over a field of characteristic 0,
R be embedded as a subring in
S, and
F
:S→S
be an endomorphism such that
F(
R)⊂
R. Suppose that every ideal of height 1 in
R generates a proper ideal in
S, and the spectrum of
R has no self-intersection points. We show that if
F is an automorphism so is
F|
R
:R→R
. When
R and
S have the same transcendence degree then the fact that
F|
R
is an automorphisms implies that
F is an automorphism.
