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.