What is the smallest field $F$ satisfying 1. and 2.?
- It is a field containing $\mathbb{Q}$
- If $ x>0, x \in F$ and $n\in\mathbb{N}$, then $x^{1/n} \in F$
In other words, $F$ is the smallest field closed under any positive n-th root.
Clearly, $F$ is a subset of $\mathbb{R}$. It doesn't have any imaginary number.
I guess such $F$ has a certain name.
Can you give me a link for more information (importance or interesting property) about $F$ ?
