I have been working with Kähler differentials, and I have $\Omega^1\_{B/k}$, where B is a commutative $k$-algebra, and $k$ is a field. I was wondering that for $d(b)=0$, does this imply that $b\in k$? I know that there are examples, however, like in $\Omega^1\_{\mathbb{R}/\mathbb{Z}}$ we have that $d(\alpha)=0$ iff $\alpha$ is algebraic. But since I am over a field, I thought maybe this will force $b\in k$ in my case? Any hint or guidance would be most helpful!