This may seem like a basic question but I can't seem to find any good texts on the matter (perhaps someone can suggest any?). Basically I have a noncommutative ring $R$ with prime ideal $\mathfrak{p}$. Obviously if $R$ was commutative then $R_\mathfrak{p}$ is a local ring. I was wondering if the same holds true for a noncommutative ring.
2026-03-25 13:53:44.1774446824
Is $R_\mathfrak{p}$ local when $R$ is noncommutative?
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