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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).

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
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).
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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