Differential polynomial rings over rings satisfying a polynomial identity

作者：Bell Jason P^*; Madill Blake W; Shinko Forte

来源：Journal of Algebra, 2015, 423: 28-36.

DOI：10.1016/j.jalgebra.2014.09.039

• Differential polynomial ring
• PI ring
• Jacobson radical

Let R be a ring satisfying a polynomial identity and let delta be a derivation of R. We show that if R is locally nilpotent then R[x; delta] 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; delta] is equal to N[x; delta], where N is the nil radical of R.

• 出版日期2015-2-1