@article{BELL201528,
    Abstract = {Let R be a ring satisfying a polynomial identity and let δ be a derivation of R. We show that if R is locally nilpotent then R[x;δ] is locally nilpotent. This affirmatively answers a question of Smoktunowicz and Ziembowski. As a consequence we have that if R is a unital PI algebra over a field of characteristic zero then the Jacobson radical of R[x;δ] is equal to N[x;δ], where N is the nil radical of R.},
    Author = {Bell, Jason P. and Madill, Blake W. and Shinko, Forte},
    File = {Differential polynomial rings over rings satisfying a polynomial identity - 1-s2.0-S0021869314005869-main.pdf},
    ISSN = {0021-8693},
    Journal = {Journal of Algebra},
    Keywords = {Differential polynomial ring, PI ring, Jacobson radical},
    Pages = {28-36},
    Title = {Differential polynomial rings over rings satisfying a polynomial identity},
    URL = {https://www.sciencedirect.com/science/article/pii/S0021869314005869},
    Volume = {423},
    Year = {2015},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0021869314005869},
    bdsk-url-2 = {https://doi.org/10.1016/j.jalgebra.2014.09.039},
    date-added = {2023-02-21 16:03:13 +0100},
    date-modified = {2023-02-21 16:03:13 +0100},
    doi = {10.1016/j.jalgebra.2014.09.039}
}

@article{BELL201528, Abstract = {Let R be a ring satisfying a polynomial identity and let δ be a derivation of R. We show that if R is locally nilpotent then R[x;δ] is locally nilpotent. This affirmatively answers a question of Smoktunowicz and Ziembowski. As a consequence we have that if R is a unital PI algebra over a field of characteristic zero then the Jacobson radical of R[x;δ] is equal to N[x;δ], where N is the nil radical of R.}, Author = {Bell, Jason P. and Madill, Blake W. and Shinko, Forte}, File = {Differential polynomial rings over rings satisfying a polynomial identity - 1-s2.0-S0021869314005869-main.pdf}, ISSN = {0021-8693}, Journal = {Journal of Algebra}, Keywords = {Differential polynomial ring, PI ring, Jacobson radical}, Pages = {28-36}, Title = {Differential polynomial rings over rings satisfying a polynomial identity}, URL = {https://www.sciencedirect.com/science/article/pii/S0021869314005869}, Volume = {423}, Year = {2015}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0021869314005869}, bdsk-url-2 = {https://doi.org/10.1016/j.jalgebra.2014.09.039}, date-added = {2023-02-21 16:03:13 +0100}, date-modified = {2023-02-21 16:03:13 +0100}, doi = {10.1016/j.jalgebra.2014.09.039} }