Let $R$ be a commutative algebra over a field $k$. Denote the $R$-module of Kahler differentials by $\Omega^1_kR$; this is the $R$-module generated by symbols of the form $da$, $a\in R$, and relations $$ d(\lambda a+b)=\lambda da+db,\;\;\; dab =adb+bda,\;\;\; d1=0, \;\;\; \forall a,b\in A, \lambda\in k$$ The $R$-module of $i$-forms is the $i$th exterior power $\Omega^i_kR:= \Lambda^i_k\Omega^1_kR$.

When $R$ has Krull dimension $n$, call $\Omega^n_kR$ the module of **volume forms**. When $R$ is the coordinate ring of a smooth affine variety $X$ of dimension $n$, then elements of $\Omega^nR$ determine volume forms on $X$.

For singular varieties, the behavior of $\Omega^nR$ can be weirder. For example, the simple cusp in the plane $$R=\mathbb{C}[x,y]/x^3-y^2$$ has a volume form $3ydx-2xdy$ which is non-zero, but $$y(3ydx-2xdy) = 3x^3dx-2xydy = xd(x^3)-xd(y^2)=0$$ So, the module $\Omega^1_kR$ of volume forms here has a torsion element.

My question is:
**Under what conditions on $R$ is $\Omega^n_kR$ torsion-free?**