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.