Geodesic
On the dimension of noncommutative affine algebras
Izvestiya. Mathematics, Tome 7 (1973) no. 2, pp. 281-285 
V. T. Markov. On the dimension of noncommutative affine algebras. Izvestiya. Mathematics, Tome 7 (1973) no. 2, pp. 281-285. http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a1/
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     title = {On the dimension of noncommutative affine algebras},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $R$ be a finitely generated prime $PI$-algebra over a field $F$. $Z$ is the center of its ring of fractions. It is proved that $Z$ is the field of fractions of the center of $R$ and that the transcendence degree of $Z$ over $F$ is equal to the maximal length of a chain of prime ideals in $R$.

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