All Questions

Let $k[X] = k[x_1,\ldots, x_n]$ be the polynomial ring over a field of characteristic zero. Assume that $(D_1,\ldots, D_n)$ is a $k[X]$-basis of $\text{Der}_k(k[X])$. Suppose that the vector space $\...

For a smooth affine variety $\operatorname{Spec} A$ over a ring $R$ we have an algebra of differential operators $\mathcal{D}_A$ (here I mean not the Grothendieck differential operators but PD-ones). ...

Given a commutative associative unital algebra over a field of characteristic zero. Is it true that any derivation of it preseves its nil-radical? More explicitly, let $D$ be a derivation of an ...

Let $k$ be a field of characteristic zero and $A$ be a $k$-algebra. A derivation on $A$ is a $k$-linear map $D: A \to A$ such that $D(ab)=aD(b)+bD(a), \forall a,b \in A$. A derivation is called ...