Geodesic
On Hilbert series and the homology of PI-algebras
Sbornik. Mathematics, Tome 189 (1998) no. 11, pp. 1685-1700

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The main goal of this paper is to generalize the criterion for complete intersections well known in commutative algebra to the case of an arbitrary variety of PI-(super)algebras. As a consequence, formulae are obtained for computing the Hilbert series of the even and odd parts of relatively free superalgebras and free special Jordan superalgebras. 
@article{SM_1998_189_11_a4,
     author = {D. I. Piontkovskii},
     title = {On {Hilbert} series and the homology of {PI-algebras}},
     journal = {Sbornik. Mathematics},
     pages = {1685--1700},
     publisher = {mathdoc},
     volume = {189},
     number = {11},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_11_a4/}
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D. I. Piontkovskii. On Hilbert series and the homology of PI-algebras. Sbornik. Mathematics, Tome 189 (1998) no. 11, pp. 1685-1700. http://geodesic.mathdoc.fr/item/SM_1998_189_11_a4/