Geodesic
A Characterization of Varieties of Associative Algebras of Exponent two
Serdica Mathematical Journal, Tome 26 (2000) no. 3, pp. 245-252

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It was recently proved that any variety of associative algebras over a field of characteristic zero has an integral exponential growth. It is known that a variety V has polynomial growth if and only if V does not contain the Grassmann algebra and the algebra of 2 × 2 upper triangular matrices. It follows that any variety with overpolynomial growth has exponent at least 2. In this note we characterize varieties of exponent 2 by exhibiting a finite list of algebras playing a role similar to the one played by the two algebras above.
Keywords: Variety of Algebras, Polynomial Identity 
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Giambruno, A.; Zaicev, M. A Characterization of Varieties of Associative Algebras of Exponent two. Serdica Mathematical Journal, Tome 26 (2000) no. 3, pp. 245-252. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_3_a4/