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Let F be a field and A a free associative F-algebra or a group algebra of afree group with an infinite set X of generators. We find a necessary andsufficient condition for the inclusion I' into I, where I=I_1...I_k andI'=I'_1...I'_l are any products of T-ideals in A. A canonical reformulation interms of products of group representation varieties answers a question posed in1986

On products of T-ideals in free algebras and free group algebras