Simple extension

Remarks

The extensions $\mathbb{C}/\mathbb{R}$, generated by $i$, and $\mathbb{Q}(\sqrt{2})/\mathbb{Q}$, generated by $\sqrt{2}$, are simple. The extension $\mathbb{Q}(\sqrt{3}, \sqrt{7})/\mathbb{Q}$ is simple, with the generator $\sqrt{3} + \sqrt{7}$. By the primitive element theorem, every finite separable extension is simple. For finite fields, the term "primitive element" usually means a generator of the multiplicative group, which is a stronger condition.