Abstract
Let K be a commutative noetherian ring. It is proved that a representation of a finite group on a K-module of finite length or on a K-module of finite exponent has a finite basis for its identities. In particular, this implies an earlier result of Nguyen Hung Shon and the author stating that every representation of a finite group over a field is finitely based. The problem whether every representation of a finite group over a commutative noetherian ring is finitely based still remains open.
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