= Conormal module
{title2=$I/I^2$}
For an <ideal> $I\subseteq R$, its conormal module is $I/I^2$, naturally an $R/I$-<module>. It records generators and relations to first order along the quotient $R/I$. If $I$ is the <maximal ideal> of a <local ring>, it is the <cotangent space of a local ring> over the <residue field>. For the augmentation ideal $(X_1-1,\ldots,X_r-1)$ of $A[X_1^{\pm1},\ldots,X_r^{\pm1}]$, reduction modulo $I^2$ gives $I/I^2\cong A^r$, with basis the classes of $X_i-1$.
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