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Let KG be the group ring of a polycyclic-by-finite group G over a field K of characteristic zero, R be the Goldie ring of fractions of KG, S be an arbitrary subring of R n×n . We prove that the intersection of the commutator subring [S, S] with the center Z(S) is nilpotent. This implies the existence of a nontrivial trace function in R n×n

Trace functions in the ring of fractions of polycyclic group rings