Regev, Amitai 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 Cited in 3 Documents MSC: 16Rxx Rings with polynomial identity 16S50 Endomorphism rings; matrix rings Keywords:trace identities; generating functions; trace cocharacters; codimension of matrices; semiprime varieties; prime variety Citations:Zbl 0644.00007 × Cite Format Result Cite Review PDF