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Let E be a finite extension of R. Use the fact that C is algebraicallyclosed to prove that E = C or E = R.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 14E: 14. Let be an ideal in a ring with unity . Prove that if then .

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Let E be a finite extension of R. Use the fact that C is algebraically
closed to prove that E = C or E = R.

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