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Title: A Characterization of Varieties of Associative Algebras of Exponent two
Authors: Giambruno, A.
Zaicev, M.
Keywords: Variety of Algebras
Polynomial Identity
Issue Date: 2000
Publisher: Institute of Mathematics and Informatics
Citation: Serdica Mathematical Journal, Vol. 26, No 3, (2000), 245p-252p
Abstract: 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.
Description: ∗The first author was partially supported by MURST of Italy; the second author was par- tially supported by RFFI grant 99-01-00233.
ISSN: 1310-6600
Appears in Collections:Volume 26 Number 3

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