Geodesic
Graded algebras
Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 197-204 
V. E. Govorov. Graded algebras. Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 197-204. http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a11/
@article{MZM_1972_12_2_a11,
     author = {V. E. Govorov},
     title = {Graded algebras},
     journal = {Matemati\v{c}eskie zametki},
     pages = {197--204},
     year = {1972},
     volume = {12},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a11/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the growth in the number of dimensions $d_n$ of the homogeneous component of a graded algebra with a finite number of defining relations and generators for the Poincaré series $\sum d_nx^n$. It is proved that if the defining relations are words, the Poincaré series is a rational function. In the general case inequalities are proved linking the number of dimensions $d_n$ with the number of generators defining relations and their degree.