algebra

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

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algebra

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