There seems to be another version of Artin-Whaples Theorem, called the Artin-Whaples Approximation theorem.
The theorem stated here is Artin-Whaples Theorem for central simple algebras.
Artin-Whaples Theorem: Let be a central simple algebra over a field . Let be linearly independent over and let be any elements in . Then there exists for such that the -linear map defined by satisfies for all .
Very nice and useful theorem.