System of parameters

Definition

Let $R$ be a local ring and let $d$ be the Krull dimension of $R$. Then, a system of parameters for $R$ is a system of $d$ elements $x_{1},x_{2},\ldots ,x_{d}$ such that there exists a $n$ for which the $n^{th}$ power of the maximal ideal lies inside the ideal generated by the $x_{i}$s.

Facts

The dimension of $R$ is actually the smallest $d$ for which such a system of $x_{i}$s could occur.