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ON THE CODIMENSION GROWTH OF G-GRADED ALGEBRAS

By Eli Aljadeff

Abstract

Abstract. Let W be an associative PI affine algebra over a field F of characteristic zero. Suppose W is G-graded where G a finite group. Let exp(W) and exp(We) denote the codimension growth of W and We respectively. (Here We, (e ∈ G) denotes the identity component of W.) We prove exp(W) ≤ | G | 2 exp(We). This was conjectured by in Y. A. Bahturin and M. V. Zaicev, Identities of graded algebras and codimension growth, Trans. Amer. Math. Soc. 356 (2004), no. 10, 3939–3950. 1

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