а) Check whether or not Q(/5)- Q(/7). b) Check whether or not if L/K and K/F are Galois extensions, then L/F is a Galois extension. Give an example, with justification, of a reducible separable polynomial over F25. c) d) Find the splitting field of x° - 4, and its degree, over Q.
а) Check whether or not Q(/5)- Q(/7). b) Check whether or not if L/K and K/F are Galois extensions, then L/F is a Galois extension. Give an example, with justification, of a reducible separable polynomial over F25. c) d) Find the splitting field of x° - 4, and its degree, over Q.
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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Transcribed Image Text:6.
а)
Check whether or not Q(/5)= Q(/7).
b)
Check whether or not if L/K and K/F are Galois extensions, then L/F is a
Galois extension.
c)
Give an example, with justification, of a reducible separable polynomial
over F125.
6.
d)
Find the splitting field of x° - 4, and its degree, over Q.
7.
i)
Show that Q(2/4,i)/Q is a Galois extension.
ii)
Find the structure of its Galois group, G.
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