## If the Localization is Noetherian for All Prime Ideals, Is the Ring Noetherian?

## Problem 617

Let $R$ be a commutative ring with $1$.

Suppose that the localization $R_{\mathfrak{p}}$ is a Noetherian ring for every prime ideal $\mathfrak{p}$ of $R$.

Is it true that $A$ is also a Noetherian ring?