The discussion revolves around proving a statement regarding maximal ideals in the context of quotient rings. Specifically, it examines the relationship between a maximal ideal in a ring and its corresponding ideal in a quotient ring formed by another ideal.
The discussion includes various perspectives on the validity of the original statement and the application of the fourth isomorphism theorem. While some participants express confidence in the statement, others introduce additional considerations that may complicate the proof. There is an ongoing exploration of ideas without a clear consensus.
Participants are navigating the implications of the fourth isomorphism theorem and its relevance to the proof. There is also a mention of polynomial irreducibility that introduces a potential constraint on the discussion.
micromass said:This statement is 100% correct. So don't worry about it.
Have you heard of the fourth isomorphism theorem (you probably didn't call it that). It states that there is a bijective correspondance between ideals of R that contain I and ideals of R/I.
In particular, if J is an ideal of R/I, then J=J'/I for some ideal J' of R.
This is the thing you have to use to prove this question. If you didn't see it, then perhaps you could try to prove it...