The Next Inequality

Considering it has been at least a post removed, I'll bring us back to our situation. We have a local Noetherian ring $latex (R, \frak{m})$. Our notation is that $latex \delta(R)$ is the least number of generators of an $latex \frak{m}$-primary ideal (which was shown to be independent of choice of ideal here). The goal… Continue reading The Next Inequality


Applying the Hilbert Polynomial

Let's start applying to some specific situations now. Suppose $latex R$ is a Noetherian local ring with maximal ideal $latex \frak{m}$. Let $latex \frak{q}$ be an $latex \frak{m}$-primary ideal. Let $latex M$ be a finitely-generated $latex R$-module, and $latex (M_n)$ a stable $latex \frak{q}$-filtration of $latex M$. Don't panic from the set-up. I think I… Continue reading Applying the Hilbert Polynomial