On codimension growth of finitely generated associative algebras

被引：162
|
作者：
Giambruno, A [1 ]
Zaicev, M
机构：
[1] Univ Palermo, Dipartimento Matemat & Applicaz, I-90123 Palermo, Italy
[2] Moscow MV Lomonosov State Univ, Fac Math & Mech, Dept Algebra, Moscow 119899, Russia
来源：
ADVANCES IN MATHEMATICS | 1998年 / 140卷 / 02期
关键词：
D O I：
10.1006/aima.1998.1766
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let A be a PI-algebra over a field F. We study the asymptotic behavior of the sequence of codimensions c(n)(A) of A. We show that if A is finitely generated over F then Inv (A)=lim(n-->infinity) n root c(n)(A) always exists and is an integer. We also obtain the following characterization of simple algebras: A is finite dimensional central simple over F if and only if Inv(A) = dim A. (C) 1998 Academic Press.
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页码：145 / 155
页数：11
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