Remark 2: Note that there can be several fields of order p". However, theywill all be isomorphic, not equal. For example, you can check that x² +1 and_F,[x]/B₂(x)/(x² + 1)andx²-x-1 are both irreducible over F. Hence K =L= F₂[x]/5(x ) (x²-x-1) are both fields having 9 elements. Hence both arehow do we get this2isomorphic to F. But KL, since, for example, x² +1=0 in K, butx²+1=x+2+Ō in L.

Answered: Image /qna-images/answer/4aa00b10-9186-4a93-b721-3a67ce343ab7.jpg

Answered: Remark 2: Note that there can be…

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 6E: In Exercises , a field , a polynomial over , and an element of the field obtained by adjoining a...

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