If $A$ is a Noetherian local ring with maximal ideal $\mathfrak m$, how do you show that $\mathfrak m^{i}/\mathfrak m^{i+1}$ is a finitely-generated $A/\mathfrak m$-module/vector space?
I know each $\mathfrak m^i$ (and each $\mathfrak m^{i}/\mathfrak m^{i+1}$) is a f.g. $A$-module...