Abstract
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 ′ ⊆ 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 varieties of representations of groups answers a question posed in 1986 [A.Yu. Olshanskii, An addition to the Neumanns–Shmel’kin theorem, Matem., Mekhan. Vestnik Moskovskogo Universiteta 6 (1986) 61–64 (in Russian)].
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