uniformizer

《Local Fields》 · 第 5 页 · Chapter I，Section 1「Definition of Discrete Valuation Ring」

A ring $A$ is called a discrete valuation ring if it is a principal ideal domain that has a unique non-zero prime ideal $\mathfrak m(A)$. [...] In a principal ideal domain, the non-zero prime ideals are the ideals of the form $\pi A$, where $\pi$ is an irreducible element. The definition above comes down to saying that $A$ has one and only one irreducible element, up to multiplication by an invertible element; such an element is called a uniformizing element of $A$ (or uniformizer; Weil [123] calls it a “prime element”).