what is this property called?(Field theory)

Question

In what references the following property $P$ of a field $F$ is investigated?

The property $P$: For all $n\in \mathbb{N}$ if $\sum_{i=1}^{n} f_{i}^{2}=0,\;\;f_{i}\in F$ then $f_{i}=0, \forall i\in \{1,2,\ldots,n\}$

Answer 1

Such a field is called Formally Real.