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From Lemma 1.1.8, we obtain the following: Assume that $R \subseteq S$ are commutative rings and $u: R[x,y] \to R[x,y]$ is an $R$-algebra endomorphism that has an invertible Jacobian, namely, $Jac(u(x)...

Let $A_1:=A_1(x,y,k)$ be the first Weyl algebra over a field $k$ of characteristic zero, namely, the $k$-algebra generated by $x$ and $y$ with relation $yx-xy=1$. Let $f:(x,y) \mapsto (p,q)$ be a $k$-...