Geodesic
Identities of finitely generated algebras over an infinite field
Izvestiya. Mathematics , Tome 37 (1991) no. 1, pp. 69-96.

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It is proved that for each finitely generated associative PI-algebra $U$ over an infinite field $F$, there is a finite-dimensional $F$-algebra $C$ such that the ideals of identities of the algebras $U$ and $C$ coincide. This yields a positive solution to the local problem of Specht for algebras over an infinite field: A finitely generated free associative algebra satisfies the maximum condition for $T$-ideals. 
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A. R. Kemer. Identities of finitely generated algebras over an infinite field. Izvestiya. Mathematics , Tome 37 (1991) no. 1, pp. 69-96. http://geodesic.mathdoc.fr/item/IM2_1991_37_1_a3/

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