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On the dimension of graded algebras

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Abstract

To each graded algebra R with a finite number of generators we associate the series T(R, z) = ∑dnzn, where dn is the dimension of the homogeneous component of R. It is proved that if the dimensions dn 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.

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Additional information

Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 209–216, August, 1973.

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Govorov, V.E. On the dimension of graded algebras. Mathematical Notes of the Academy of Sciences of the USSR 14, 678–682 (1973). https://doi.org/10.1007/BF01147113

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Keywords

  • Finite Number
  • Polynomial Growth
  • Homogeneous Component