Suppose we have a noncommutative ring $R$ and multiplicatively closed set that is both right Ore, and right reversible, i.e. it is a right denominator set. Now, we can localize $R$ at $S$ to form $RS^{-1}$. If $R$ is commutative and $S$ is a prime ideal, then I know $RS^{-1}$ is local, but when is this true for $R$ noncommutative and $S$ as above? Is it ever true for a general class of rings, such as when $R$ is Noetherian?
2026-03-25 13:51:45.1774446705
When is $RS^{-1}$ a local ring?
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