Definition
Let E/F be a field extension, α an element of E, and F the ring of polynomials in x over F. The minimal polynomial of α is the monic polynomial of least degree among all polynomials in F having α as a root; it exists when α is algebraic over F, that is, when f(α) = 0 for some non-zero polynomial f(x) in F.
Read more about this topic: Minimal Polynomial (field Theory)
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