Let A be an associative PI-algebra over a field F of characteristic zero. By studying the exponential behavior of the sequence of codimensions [c n (A)] of A, we prove that Inv(A)=lim n Γ n c n (A) always exists and is an integer. We also give an explicit way for computing such integer: let B be a f
β¦ LIBER β¦
The sequence of codimensions of PI-algebras
β Scribed by S. A. Amitsur
- Book ID
- 112885346
- Publisher
- The Hebrew University Magnes Press
- Year
- 1984
- Tongue
- English
- Weight
- 712 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0021-2172
No coin nor oath required. For personal study only.
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By the Giambruno-Zaicev theorem for associative p.i. algebras, the exponential rate of growth of the codimensions of such a p.i. algebra is always a positive integer. Here we calculate that integer for various generic p.i. algebras which are given by a single identity. These include Capelli-type id