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On the dimension of graded algebras

V. E. Govorov

Moscow Institute of Electronic Engineering

Abstract: To each graded algebra $R$ with a finite number of generators we associate the series $T(R,z)=\sum d_nz^n$, where $d_n$ is the dimension of the homogeneous component of $R$. It is proved that if the dimensions $d_n$ have polynomial growth, then the Krull dimension of $R$ cannot exceed the order of the pole of the series $T(R,z)$ for $z=1$ by more than 1.

UDC: 512

Received: 03.01.1972

 English version: Mathematical Notes, 1973, 14:2, 678–682

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