Example 1

Regular noetherian local rings of dimension 0 (resp. 1) are fields (resp. discrete valuation rings) (VI, § 3, No. 6, Prop. 9 and Cor. 1 of Theorem 1 below). Let $A$ be a discrete valuation ring; then an element $t$ of $\mathfrak{m}_A$ is a uniformizer if and only if $\{ t \}$ is a system of coordinates of $A$.