Mathematical Research Letters

Volume 6 (1999)

Number 2

Polycyclic-by-finite group algebras are catenary

Pages: 183 – 194

DOI: http://dx.doi.org/10.4310/MRL.1999.v6.n2.a6

Authors

Edward S. Letzter (Texas A & M University)

Martin Lorenz (Temple University)

Abstract

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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