= Solution
A finite extension $L/K$ of non-Archimedean <local fields> is an <unramified extension> when its <ramification index> is one and its <residue-field degree> equals $[L:K]$. Equivalently, its maximal ideal is generated by a <uniformizer> of $K$ and its residue-field extension is separable.
A finite extension of <number fields> is an <everywhere unramified extension of number fields> when every nonzero prime ideal of $K$ is unramified in $L$. Under the convention that includes infinite places, one also requires every real embedding of $K$ to remain real.
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