Abstract
The exponent $\mbox{exp}(A)$ of a PI-algebra $A$ in characteristic zero is an integer measuring the exponential rate of growth of the sequence of codimensions of $A$ (\cite{gz1,gz2}). In this paper we study the exponential rate of growth of the sequences of proper codimensions and Lie codimensions of an associative PI-algebra. We prove that the corresponding proper exponent exists for all PI-algebras, except for some algebras of exponent two strictly related to the Grassmann algebra. We also prove that the Lie exponent exists for any finitely generated PI-algebra. The value of both exponents is always equal to $\mbox{exp}(A)$ or $\mbox{exp}(A)-1$.
Lingua originale | English |
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pagine (da-a) | 1933-1962 |
Numero di pagine | 29 |
Rivista | Journal of Algebra |
Volume | 320 |
Stato di pubblicazione | Published - 2008 |
All Science Journal Classification (ASJC) codes
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