On Codimension Growth of Finitely Generated Associative Algebras |
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| Authors: | A Giambruno M Zaicev |
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| Institution: | aDipartimento di Matematica e Applicazioni, Università di Palermo, 90123, Palermo, Italyf1;bDepartment of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russiaf2 |
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| 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→∞
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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