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- Jun 22, 2012

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Proposition 15 reads as follow:

**Proposition 15.**The maximal ideals in F[x] are the ideals (f(x)) generated by irreducible polynomials. In particular, F[x]/(f(x)) is a field if and only if f(x) is irreducible.

Dummit and Foote give the proof as follows:

*This follows from Proposition 7 of Section 8.2 applied to the Principal Ideal Domain F[x].*

**Proof:****- can someone show me how Proposition 15 above follows from Proposition 7 of Section 8.2 (see below for Proposition 7 of Section 8.2)**

My problem

My problem

I would be grateful for any help or guidance in this matter.

Peter

**Dummit and Foote - Section 8.2 - Proposition 7**

Proposition 7. Every nonzero prime ideal in a Principal Ideal Domain is a maximal ideal.

[This problem has also been posted on MHF]