A Characterization of Varieties of Associative Algebras of Exponent two

Giambruno, 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 -