Let F be a field and α an element not in F such that α^3 - 3α + 2 = 0. Consider the field extension F(α) which consists of all elements of the form a + bα + cα^2, where a, b, and c are elements of F. Find the multiplicative inverse of the element 2 + α in the field F(α).

Let F be a field and α an element not in F such that α^3 - 3α + 2 = 0. Consider the field extension F(α) which consists of all elements of the form a + bα + cα^2, where a, b, and c are elements of F. Find the multiplicative inverse of the element 2 + α in the field F(α).

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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Question

Let F be a field and α an element not in F such that α^3 - 3α + 2 = 0. Consider the field extension F(α) which consists of all elements of the form a + bα + cα^2, where a, b, and c are elements of F.

Find the multiplicative inverse of the element 2 + α in the field F(α).

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