Let $R$ be a ring satisfying a polynomial identity and let $D$ be aderivation of $R$. We consider the Jacobson radical of the skew polynomial ring$R[x;D]$ with coefficients in $R$ and with respect to $D$, and show that$J(R[x;D])\cap R$ is a nil $D$-ideal. This extends a result of Ferrero,Kishimoto, and Motose, who proved this in the case when $R$ is commutative.
展开▼
机译：假设$ R $是满足多项式恒等式的环，而$ D $是$ R $的推导。我们考虑了偏多项式环$ R [x; D] $的Jacobson根，其系数为$ R $且相对于$ D $，证明$ J（R [x; D]）\ cap R $为理想的零D $$。这扩展了费列罗，岸本元和Motose的结果，他们在$ R $是可交换的情况下证明了这一点。
展开▼
