Let K be an extension of F. Suppose that E1 and E2 are contained inK and are extensions of F. If [E1:F] and [E2:F] are both prime,show that E1 = E2 or E1 ∩ E2 = F.

Answered: Let K be an extension of F. Suppose…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let K be an extension of F. Suppose that E₁ and E₂ are contained in
K and are extensions of F. If [E₁:F] and [E2:F] are both prime,
show that E₁ = E₂ or E1 ∩ E2 = F.

Expert Solution

Step 1

Given: K is extension of F. $E_{1} a n d E_{2}$ are contained in K and are extension of F.
To show : $E_{1} = E_{2} o r E_{1} \cap E_{2} = F$

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