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Prove that if p is a prime, then the field Zp is not algebraically closed
Chapter 32, Problem 32.6(choose chapter or problem)
QUESTION:
Prove that if p is a prime, then the field Zp is not algebraically closed.
Questions & Answers
QUESTION:
Prove that if p is a prime, then the field Zp is not algebraically closed.
ANSWER:Step 1 of 2
Suppose F is a finite field with n elements. Then the field F can be defined as:
Construct a polynomial
The polynomial will never be zero in the field . There exists a polynomial which has no zero in the field