Embedding dimension
= Embedding dimension
{title2=$\operatorname{edim}R$}
The embedding dimension of a <Noetherian local ring> $(R,\mathfrak m)$ is $\dim_{R/\mathfrak m}(\mathfrak m/\mathfrak m^2)$. It counts the smallest number of local generators needed for the <maximal ideal>. It is at least the <Krull dimension>; equality characterizes a <regular local ring>.