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Prove that, if K is an extension field of F, then [K:F] =

Problem 29E Chapter 21

Contemporary Abstract Algebra | 8th Edition

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Problem 29E

Prove that, if K is an extension field of F, then [K:F] = n if and only if K is isomorphic to Fn as vector spaces. (See Exercise 27 in Chapter 19 for the appropriate definition. This exercise is referred to in this chapter.)

Reference:

Define the vector space analog of group homomorphism and ring homomorphism. Such a mapping is called a linear transformation. Define the vector space analog of group isomorphism and ring isomorphism.

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ISBN: 9781133599708

The full step-by-step solution to problem: 29E from chapter: 21 was answered by , our top Math solution expert on 07/25/17, 05:55AM. This full solution covers the following key subjects: Vector, isomorphism, analog, Chapter, define. This expansive textbook survival guide covers 34 chapters, and 2038 solutions. Contemporary Abstract Algebra was written by and is associated to the ISBN: 9781133599708. This textbook survival guide was created for the textbook: Contemporary Abstract Algebra , edition: 8th. Since the solution to 29E from 21 chapter was answered, more than 225 students have viewed the full step-by-step answer. The answer to “Prove that, if K is an extension field of F, then [K:F] = n if and only if K is isomorphic to Fn as vector spaces. (See Exercise 27 in Chapter 19 for the appropriate definition. This exercise is referred to in this chapter.)Reference:Define the vector space analog of group homomorphism and ring homomorphism. Such a mapping is called a linear transformation. Define the vector space analog of group isomorphism and ring isomorphism.” is broken down into a number of easy to follow steps, and 73 words.

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