Polycyclic-by-finite group algebras are catenary

We show that group algebras $kG$ of polycyclic-by-finite groups $G$, where $k$ is a field, are catenary: If $P = I_0 \subsetneq I_1 \subsetneq \cdots \subsetneq I_m = P'$ and $P = J_0 \subsetneq J_2 \subsetneq \cdots \subsetneq J_n = P'$ are both saturated chains of prime ideals of $kG$, then $m = n$.

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Published 1 January 1999