# A Characterization of Varieties of Associative Algebras of Exponent two

Serdica Mathematical Journal (2000)

- Volume: 26, Issue: 3, page 245-252
- ISSN: 1310-6600

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topGiambruno, A., and Zaicev, M.. "A Characterization of Varieties of Associative Algebras of Exponent two." Serdica Mathematical Journal 26.3 (2000): 245-252. <http://eudml.org/doc/11492>.

@article{Giambruno2000,

abstract = {∗The first author was partially supported by MURST of Italy; the second author was par-
tially supported by RFFI grant 99-01-00233.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.},

author = {Giambruno, A., Zaicev, M.},

journal = {Serdica Mathematical Journal},

keywords = {Variety of Algebras; Polynomial Identity; algebras with polynomial identities; varieties of algebras; codimensions of polynomial identities; codimension growth; exponents},

language = {eng},

number = {3},

pages = {245-252},

publisher = {Institute of Mathematics and Informatics},

title = {A Characterization of Varieties of Associative Algebras of Exponent two},

url = {http://eudml.org/doc/11492},

volume = {26},

year = {2000},

}

TY - JOUR

AU - Giambruno, A.

AU - Zaicev, M.

TI - A Characterization of Varieties of Associative Algebras of Exponent two

JO - Serdica Mathematical Journal

PY - 2000

PB - Institute of Mathematics and Informatics

VL - 26

IS - 3

SP - 245

EP - 252

AB - ∗The first author was partially supported by MURST of Italy; the second author was par-
tially supported by RFFI grant 99-01-00233.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.

LA - eng

KW - Variety of Algebras; Polynomial Identity; algebras with polynomial identities; varieties of algebras; codimensions of polynomial identities; codimension growth; exponents

UR - http://eudml.org/doc/11492

ER -

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