×

On the codimensions of matrix algebras. (English) Zbl 0676.16016

Algebra: some current trends, Proc. 5th Natl. Sch. Algebra, Varna/Bulg. 1986, Lect. Notes Math. 1352, 162-172 (1988).
[For the entire collection see Zbl 0644.00007.]
The author reviews some results of Razmyslov-Procesi theory on trace identities, his results and results of Formanek about the generating functions and the trace cocharacters. In particular, there is an asymptotic formula for the codimension of matrices. The author summarizes results of Kemer about the structure of prime and semiprime varieties and deduces values for the limits \(\lim_{n\to \infty}c_ n(A)^{1/n}\), where A is one of the following algebras \(M_ k(F)\), \(M_ k(E)\), \(E_{k,e}\) (any of these algebras generates a prime variety).
Reviewer: Yu.N.Mal’tsev

MSC:

16Rxx Rings with polynomial identity
16S50 Endomorphism rings; matrix rings

Citations:

Zbl 0644.00007