Kähler differentials

Summary

The module of Kähler differentials $\Omega_{A/R}$ of an algebra $A$ over a commutative ring $R$ is the algebraic version of the module of differential $1$-forms. It is generated by symbols $da$ for $a \in A$, subject only to the rules of differentiation. It is the universal target of derivations of $A$ over $R$. It is the basic tool to define smooth, unramified and étale maps of rings without any analysis.