#4.54 Regular local ring, regular point, regular (Noetherian) scheme

!! m/m^2 with A noetherian, is perfectly in the situation of NKA lemm

(1) m is f.g as A-module by noetherian

(2) m^2 is contained in m, hence in the nilradical of A

hence NAK tells that we can lift a basis of m/ m^2 as k=A/m - vector space to a basis of m as A-module

Hence exactly the definition of regular (local) ring is that the m is generated by dimA elements.