Regular system of parameters

Definition

Let $R$ be a regular local ring, viz a local ring in which the unique maximal ideal is generated by $dim(R)$ elements. Then, a regular system of parameters is a collection of exactly $dim(R)$ elements in the maximal ideal, that generate it.

This condition is equivalent to requiring that their images modulo the square of the maximal ideal, generate the maximal ideal modulo its square, as a vector space over the residue field.