Module of Kähler differentials (${\Omega }_{B/A}$)

For a ring map $A\to B$, the module of Kähler differentials represents $A$-derivations: ${\mathrm{Hom}}_B({\Omega }_{B/A},M)\cong {\mathrm{Der}}_A(B,M)$.

For $A\to B\to C=B/I$, there is a right-exact sequencewhere $[i]\mapsto di\otimes 1$ and $db\otimes c\mapsto cd\bar{b}$.