Every element in a field extension is contained in a basis

Let F be a field, E a finite extension of F, and \alpha \in E a nonzero element. Show that there exists a basis B \subseteq E of E over F such that \alpha \in B.


Since \alpha is nonzero, \{\alpha\} is F-linearly independent. By this exercise, there is a basis B \subseteq K over F which contains \alpha.

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