Cotangent space of a local ring
= Cotangent space of a local ring
{title2=$\mathfrak m/\mathfrak m^2$}
For a <local ring> $(R,\mathfrak m)$ with <residue field> $\kappa=R/\mathfrak m$, its cotangent space is the $\kappa$-<vector space> $\mathfrak m/\mathfrak m^2$. In a <Noetherian local ring>, its <dimension> is the minimal number of generators of $\mathfrak m$, by the <Nakayama lemma>. Equality of this <dimension> with the <Krull dimension> defines a <regular local ring>.