Suppose that $L/K$ is finite algebraic extension and $\alpha$ is algebraic and separable over K. If $L/K$ is simple algebraic extension, $L(\alpha)/K$ is simple. Does the converse holds true? That is, if $L(\alpha)/K$ is simple, then $L/K$ is simple.
Finite algebraic extension and simple extension.
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field-theory
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0this is direct consequence of primitive element theorem – 2012-12-25
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0why the first assertion true??...I mean why L/K simple algebraic extension implies L(alpha)/k is also simple?? – 2014-02-26