4 Mark the following true or false, and briefly justify your answer:(a) Every finite extension of a field of characteristic zero is normal.(b) If K is a field of characteristic zero and K C MCL with L: K finite and normal,then L: M is normal.(c) If K is a field and K C M L with L: K normal, then M: K is normal.(d) Let K be a field, and let f E K[X] be a polynomial with degree d. Then [E: K] =d, where E is any splitting field of f over K.

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 2TFE

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Mark the following true or false, and briefly justify your answer: (a) Every finite extension of a field of characteristic zero is normal.