2. Let K be an extension of F and let a e K be algebraic over F. Then (i) There exists a unique monic irreducible polynomial p (x) e F (x] of least positive degree such that p (a) = 0. (ii) If g (x) e F[x] is such that g (a) = 0, then p (x) divides g (x).
2. Let K be an extension of F and let a e K be algebraic over F. Then (i) There exists a unique monic irreducible polynomial p (x) e F (x] of least positive degree such that p (a) = 0. (ii) If g (x) e F[x] is such that g (a) = 0, then p (x) divides g (x).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![2. Let K be an extension of F and let a e K be algebraic
over F. Then
(i) There exists a unique monic irreducible polynomial
p (x) e F (x] of least positive degree such that p (a) = 0.
(ii) If g (x) e F[x] is such that g (a) = 0, then p (x) divides g (x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f117386-1e0b-45e6-8bbc-1853864178df%2Fd7f84303-45f4-4df6-a7a7-0537eed93a74%2Fqqkb6qg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let K be an extension of F and let a e K be algebraic
over F. Then
(i) There exists a unique monic irreducible polynomial
p (x) e F (x] of least positive degree such that p (a) = 0.
(ii) If g (x) e F[x] is such that g (a) = 0, then p (x) divides g (x).
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