Cumulating central polynomials and identities for \(M_ n(F_ p)\) (Q753913)

Assume F is a field of characteristic zero and \(F_ p\) is the field with p elements, p a prime. Using some methods and results of \textit{E. Formanek} [Contemp. Math. 13, 41-79 (1982; Zbl 0503.16016)] the author has found a polynomial \(g\in Z[x_ 1,...,x_{n+1}]\) which is not a central polynomial for \(M_ n(F)\) but whose reduction modulo p is a central polynomial for \(M_ n(F_ p)\). Here \(M_ n(K)\) stands for the matrix algebra of order n over the ring K.