Hey I have a question about how to continue a proof in commutative algebra. Suppose you have a Ring $R$ and a maximal ideal $m$. I want to proof that $(mR_m)^n=m^nR_m$. One direction is obvious. For the other direction you take $a^n r\in m^nR_m$. It is easy to show that this is in $(mR_m)^n$ if $r$ is a unit. If it is not then it is in $m$ as everything outside of $m$ is inverted in $R_m$. But what do I do with that...I think its probably trivial, but I don't know how to finish of the proof. Thanks for the help!
2026-04-08 15:43:10.1775662990
Question about proof in commutative algebra
58 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMMUTATIVE-ALGEBRA
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