Definition 10.60.10. Let $(R, \mathfrak m)$ be a Noetherian local ring of dimension $d$.

1. A system of parameters of $R$ is a sequence of elements $x_1, \ldots , x_ d \in \mathfrak m$ which generates an ideal of definition of $R$,

2. if there exist $x_1, \ldots , x_ d \in \mathfrak m$ such that $\mathfrak m = (x_1, \ldots , x_ d)$ then we call $R$ a regular local ring and $x_1, \ldots , x_ d$ a regular system of parameters.

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