论文标题
局部nilpotent偏斜的环
Locally nilpotent skew extensions of rings
论文作者
论文摘要
我们将现有的结果扩展到局部nilpotent差分多项式环上，以偏向环的延伸。我们证明，如果$ \ Mathscr {g} = \ {σ_t\} _ {t} $ in t} $是代数$ r $，$ r $，$ \ mathscr {d} = \ {Δ_T\} $ s s y s的本地有限的自动形态家族。 $ \ r $的Prime Radical $ p $在$ \ Mathscr {d} $下是强烈不变的，那么理想的$ p \ langle t，\ Mathscr {g}，\ Mathscr {d} \ rangle^$局部尼尔氏剂。然后，我们将此结果应用于具有局部nilpotent推导的代数。我们证明，具有特征性$ 0 $的字段上的任何代数$ r $，在本地较小的派生派$ d $带有交换核的情况下，并且$ r $由$ \ ker d^2 $生成，它具有本地nilpotent nilpotent jacobson radical。
We extend existing results on locally nilpotent differential polynomial rings to skew extensions of rings. We prove that if $\mathscr{G}=\{σ_t\}_{t\in T}$ is a locally finite family of automorphisms of an algebra $R$, $\mathscr{D}=\{δ_t\}_{t\in T}$ is a family of skew derivations of $R$ such that the prime radical $P$ of $R$ is strongly invariant under $\mathscr{D}$, then the ideal $P\langle T,\mathscr{G},\mathscr{D}\rangle^*$ of $R\langle T,\mathscr{G},\mathscr{D}\rangle$, generated by $P$, is locally nilpotent. We then apply this result to algebras with locally nilpotent derivations. We prove that any algebra $R$ over a field of characteristic $0$, having a surjective locally nilpotent derivation $d$ with commutative kernel, and such that $R$ is generated by $\ker d^2$, has a locally nilpotent Jacobson radical.
