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Definition: Minimal Polynomial
Let \(F\) be a field and let \(L/F\) be its field extension. Let \(\alpha\in L\) be algebraic over \(F\). Then the monic polynomial \(p\in F[X]\) with \(p(\alpha)=0\) of minimal degree is called the minimal polynomial of \(\alpha\).
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References
Adapted from CC BYSA 3.0 Sources:
 Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück