Local Fields
《Local Fields》 · 第 19 页 · Chapter I，Section 6「Ramification Index and Residue Class Degree」，Definition
A polynomial $f=X^n+a_1X^{n-1}+\cdots+a_n$ is called an Eisenstein polynomial if it is monic, if all the $a_i$ belong to the maximal ideal $\mathfrak m$, and if $a_n\notin\mathfrak m^2$.