🚀 go-pugleaf

I am looking for a recent and explicit reference to the following:

THEOREM
	Let p_i(x_1,...,x_n), 1 <=i <= m be complex polynomials.  Then either 
(1) or (2) holds:

(1) There exists a non-zero polynomial T  in m variables so that 
	T(p_1(x_1,...,x_n),...,p_m(x_1,...,x_n)) = 0 for all (x_1,...x_n).
	(ALGEBRAIC DEPENDENCE)

		or

(2)  There exists a non-zero polynomial T  in m variables so that, if
(v_1,...,v_m) is a complex m-tuple and T(v_1,...,v_m) != 0, then there exist
(u_1,...,u_n) so that p_i(u_1,...,u_n) = v_1
	(ALGEBRAIC INDEPENDENCE)

 By the way, I know that this is a theorem, as several kind algebraic geometers
have proved for me, and I know that this is a special case of some more
sophisticated mathematics.  I am interested in a source which states the above
as explicitly as possible.  Surely this was done by one of our 19th century
friends.
 I will e-mail a summary of responses on request.

Many thanks,
Bruce Reznick