✦ LIBER ✦

On Codimension Growth of Finitely Generated Associative Algebras

✍ Scribed by A. Giambruno; M. Zaicev

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 245 KB
Volume: 140
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1766

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✦ Synopsis

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 Ä n 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.

1998 Academic Press c n (A) a: n for all n. In [6] Kemer described the algebras A in characteristic zero having polynomial growth of the codimensions in the language of the cocharacter Article No. AI981766 145

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