Geodesic
On $PI$-rings having a faithful module with Krull dimension
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 557-559

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The main result: if a $PI$-ring $R$ has a faithful left module $M$ with Krull dimension, then its prime radical $N$ is nilpotent. Moreover if the left modules $M$ and $N$ are finitely generated then $R$ has left Krull dimension which is equal to Krull dimension of the module $M$. 
@article{FPM_1995_1_2_a19,
     author = {V. T. Markov},
     title = {On $PI$-rings having a faithful module with {Krull} dimension},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {557--559},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a19/}
}
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V. T. Markov. On $PI$-rings having a faithful module with Krull dimension. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 557-559. http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a19/