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- Jun 22, 2012

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In example (3) we read (see attached)

" (3) Take [TEX] F = \mathbb{Q} [/TEX] and [TEX] p(x) = x^2 - 2 [/TEX], irreducible over [TEX] \mathbb{Q} [/TEX] by Eisenstein's Criterion, for example"

Now Eisenstein's Criterion (see other attachment - Proposition 13 and Corollary14) require the polynomial to be in R[x] where R s an integral domain.

In example (3) on page 515 of D&F we are dealing with a field, specifically [TEX] \mathbb{Q} [/TEX].

My problem is, then, how does Eisenstein's Criterion apply?

Can anyone please clarify this situation for me?

Peter

[This has also been posted on MHF]