On the dimension of graded algebras

To each graded algebra R with a finite number of generators we associate the series T(R, z) = d_nzⁿ, 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.Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 209–216, August, 1973.