Consider $A$ a domain which is a finitely generated $K$-algebra for $K$ algebraically closed (say generated by $a_1,\dots,a_n$), define $\tau_{A/K}:=\text{Hom}_A(\Omega_{A/K},A)$, I want to show that it's a finitely generated $A$-module without torsion. Do you have ideas on how to show this ?
I maybe wanted to say that $\tau_{A/K}\cong \text{Der}_K(A,A)$ and consider $d_i:A\to A$ which takes $a=P(a_1,\dots,a_n)$ to $\frac{\partial P}{\partial x_i}(a_1,\dots,a_n)$ but I'm struggling to make it work.