The Primitive Element Theorem states that any finite extension of fields can be generated by a single element. In other words, if you have a field extension of the form $K(F)$, where $F$ is a finite extension of a field $K$, there exists an element $ heta$ in $F$ such that $F = K( heta)$. This theorem connects the concepts of splitting fields and simple extensions, highlighting the structure of field extensions and making it easier to understand the relationships between fields.
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