Please help me to prove for all maximal ideals $\mathfrak{m}$ of $R$, $(aR/a^2R)_\mathfrak{m}\cong (aR)_\mathfrak{m}/(a^2R)_\mathfrak{m}\cong aR_\mathfrak{m}/a^2R_\mathfrak{m}$, where $R$ is a commutative ring with 1 and $a\in R$.
2026-04-24 08:12:18.1777018338
Congruence in localization of rings
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This is because localization is exact.