Answered: (a) Check whether or not x³ + 2x + 1 e…

(a) Check whether or not x³ + 2x + 1 e F;[x] is a primitive polynomial. (b) Let F, L, K be fields such that K/F is Galois and F CL C K. Then prove or disprove that : (i) L/F is Galois.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 20E: Prove Theorem If and are relatively prime polynomials over the field and if in , then in .

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6. (a) Check whether or not x³ + 2x + 1 € F,[x] is
a primitive polynomial.
(b)
Let F, L, K be fields such that K/F is Galois
and F C L C K. Then prove or disprove
that :
(i)
L/F is Galois.

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