Answered: Let K be an extension of a field F and…

Let K be an extension of a field F and an element a∈K be an algebraic over F. If f(x) be a minimal polynomial of a over F, then f(x) is irreducible over F.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.2: Divisibility And Greatest Common Divisor

Problem 20E

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Let K be an extension of a field F and an element a∈K be an algebraic over F.
If f(x) be a minimal polynomial of a over F, then f(x) is irreducible over F.

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