Abstract
Let c(x 1, … , x d ) be a multihomogeneous central polynomial for the n × n matrix algebra M n (K) over an infinite field K of positive characteristic p. We show that there exists a multihomogeneous polynomial c 0(x 1, … , x d ) of the same degree and with coefficients in the prime field 𝔽 p which is central for the algebra M n (F) for any (possibly finite) field F of characteristic p. The proof is elementary and uses standard combinatorial techniques only.
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Acknowledgements
The research of the first named author was partially supported by the Slovenian Research Agency (Program No. P1-0288).