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5.10. Let K/F be a finite extension of fields. Prove that there is a finite set of elements a₁,..., an E K such that K= F(a₁,..., An). (Hint. Adjoin elements one at a time and estimate the degree of the extension that you get.)

5.10. Let K/F be a finite extension of fields. Prove that there is a finite set of elements a₁,..., an E K such that K= F(a₁,..., An). (Hint. Adjoin elements one at a time and estimate the degree of the extension that you get.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**5.10.** Let \( K/F \) be a finite extension of fields. Prove that there is a finite set of elements \( \alpha_1, \ldots, \alpha_n \in K \) such that \[ K = F(\alpha_1, \ldots, \alpha_n). \] *(Hint. Adjoin elements one at a time and estimate the degree of the extension that you get.)*
Transcribed Image Text:**5.10.** Let \( K/F \) be a finite extension of fields. Prove that there is a finite set of elements \( \alpha_1, \ldots, \alpha_n \in K \) such that \[ K = F(\alpha_1, \ldots, \alpha_n). \] *(Hint. Adjoin elements one at a time and estimate the degree of the extension that you get.)*
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