Kähler differential
= Kähler differential
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{title2=$\Omega_{B/A}$}
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= Module of Kähler differentials
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For a ring map $A\to B$, the module of Kähler differentials represents $A$-derivations: $\operatorname{Hom}_B(\Omega_{B/A},M)\cong\operatorname{Der}_A(B,M)$.
For an algebra $B$ over $A$, the module $\Omega_{B/A}$ represents $A$-linear derivations: every derivation $B\to N$ factors uniquely through the universal map $d:B\to\Omega_{B/A}$.