Abstract
LetAbe a PI-algebra over a fieldF. We study the asymptotic behavior of the sequence of codimensionscn(A) ofA. We show that ifAis finitely generated overFthenInv(A)=limn→∞cn(A)always exists and is an integer. We also obtain the following characterization of simple algebras:Ais finite dimensional central simple overFif and only ifInv(A)=dim=A.
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