Trace rings for verbally prime algebras (Q1177395)

The author studies properties of the trace identities for \(M_{k,l}\) --- one of the classes of verbally prime \(PI\)-algebras. Assume the algebra \(R\) is \(PI\)-equivalent to \(M_{k,l}\) and \(J\) is the ideal of \(R\) generated by all evaluations of Razmyslov's central polynomials (cf. \textit{Yu. P. Razmyslov} [Mat. Sb., Nov. Ser. 128(170), 194-215 (1985; Zbl 0601.16016)]). The author proves that if \(J\) has zero annihilator then \(R\) is embeddable in a central extension \(R_ 1\) having a non-degenerate trace. Moreover the author proves that the ideal of trace identities for \(R_ 1\) coincides with that of \(M_{k,l}\), and, if \(r\in R_ 1\) then \(J^ nr\subset R\) for some integer \(n\). In the correction the main theorem and its proof are modified.