Exact asymptotic behaviour of the codimensions of some P.I. algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Exact asymptotic behaviour of the codimensions of some P.I. algebras

Authors:	Vesselin Drensky Amitai Regev

Institution:	(1) Institute of Mathematics, Bulgarian Academy of Sciences, Akad. G.Bonchev Str., Block 8, 1113 Sofia, Bulgaria;(2) Department of Mathematics, The Pennsylvania State University, 16802 University Park, PA, USA;(3) Department of Theoretical Mathematics, The Weizmann Institute of Science, 76100 Rehovot, Israel

Abstract:	Letc _n(A) denote the codimensions of a P.I. algebraA, and assumec _n(A) has a polynomial growth: $c_n (A)_{n_{ \to \infty }^ \simeq } qn^k$ . Then, necessarily,q∈ℚ D3]. If 1∈A, we show that $\frac{1}{{k!}} \leqslant q \leqslant \frac{1}{{2!}} - \frac{1}{{3!}} + - \cdot \cdot \cdot + \frac{{( - 1)^k }}{{k!}} \approx \frac{1}{e}$ , wheree=2.71…. In the non-unitary case, for any 0<q∈ℚ, we constructA, with a suitablek, such that $c_n (A)_{n_{ \to \infty }^ \simeq } qn^k$ . In memory of S. A. Amitsur, our teacher and friend Partially supported by Grant MM404/94 of Ministry of Education and Science, Bulgaria and by a Bulgarian-American Grant of NSF. Partially supported by NSF grant DMS-9101488.

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