Let $R$ be a commutative ring with identity, and $I \subseteq R$ any ideal.
Is it true that the maximal ideals of $R/I$ are in 1-1 correspondence with the maximal ideals of $R$ which contain $I$?
2026-04-06 07:05:37.1775459137
Maximal ideals in $R/I$ for $R$ a commutative ring
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Yes. It is part of the all-powerful and important Correspondence Theorem for rings. The is also a Correspondence Theorem for groups.