Maximal ideals in $R/I$ for $R$ a commutative ring

Question

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 $I$?

Yes. That's part of te all-powerful and important Correspondence Theorem for rings. There is also one for groups. — DonAntonio, Aug 31 '20 at 10:24
If you upgrade your comment to an answer then I will happily accept it so that this question can be listed as answered :) — Matt, Aug 31 '20 at 10:26

score 3 · Accepted Answer · answered Aug 31 '20 at 10:41

3

Yes. It is part of the all-powerful and important Correspondence Theorem for rings. The is also a Correspondence Theorem for groups.

answered Aug 31 '20 at 10:41

DonAntonio

1 Answers1