Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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True or False

1. Every nonconstant polynomial in F[x] has a root in every extension field of F, that is if K is an extension of F and f is a nonconstant polynomial in F[x], then f has a root in K.
2. There is no proper intermediate field of ℝ and ℂ, i.e. there exists no field E such that ℝ ≤ E ≤ ℂ but ℝ ≠ E, E ≠ ℂ.
3. If [K:F]=p for some prime p and F ≤ E ≤ F, then F=E.

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