  Let F be a field and A a free associative F-algebra or a group algebra of a
free group with an infinite set X of generators. We find a necessary and
sufficient condition for the inclusion I' into I, where I=I_1...I_k and
I'=I'_1...I'_l are any products of T-ideals in A. A canonical reformulation in
terms of products of group representation varieties answers a question posed in
1986
