Authors
Citation
A. Giambruno et M. Zaicev, On codimension growth of finitely generated associative algebras, ADV MATH, 140(2), 1998, pp. 145-155
Citations number
11
Categorie Soggetti
Mathematics
Journal title
ADVANCES IN MATHEMATICS
ISSN journal
00018708
→ ACNP
Volume
140
Issue
2
Year of publication
1998
Pages
145 - 155
Database
ISI
SICI code
0001-8708(199812)140:2<145:OCGOFG>2.0.ZU;2-D
Abstract
Let A be a PI-algebra over a field F. We study the asymptotic behavior of t
he sequence of codimensions c(n)(A) of A. We show that if A is finitely gen
erated over F then Inv (A)=lim(n-->infinity) n root c(n)(A) always exists a
nd is an integer. We also obtain the following characterization of simple a
lgebras: A is finite dimensional central simple over F if and only if Inv(A
) = dim A. (C) 1998 Academic Press.