Artin-Whaples Theorem

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 A be a central simple algebra over a field F. Let a_1,\dots,a_n\in A be linearly independent over F and let b_1,\dots,b_n be any elements in A. Then there exists a_i',a_i''\in A for i=1,\dots,m such that the F-linear map f:A\to A defined by f(x)=\sum_{r=1}^m a_r'xa_r'' satisfies f(a_j)=b_j for all j=1,\dots,n.

Very nice and useful theorem.

Author: mathtuition88

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