Projective Schur algebras have Abelian splitting fields
For any commutative ring \(R\), a Schur algebra \(A\) is an Azumaya \(R\)- algebra for which there is a finite group \(G\) and an \(R\)-algebra epimorphism \(f:RG\to A\). This was the generalization of the notion of a Schur algebra given and studied by \textit{F. DeMeyer} and \textit{R. Mollin} [in J. Pure Appl. Algebra 35, 117-122 (1985; Zbl 0555.13003)]. The paper under review restricts attention to the field case and the generalization of the Schur algebras to projective Schur algebras. The main result of their paper is the predictable fact that every projective Schur algebra over a field \(K\) is split by an abelian extension of \(K\). It would be interesting to investigate whether or not this holds true in the more general ring case, using theory as given for example by \textit{F. DeMeyer} and \textit{E. Ingraham} [in Separable algebras over commutative rings (Lect. Notes Math. 181, 1971; Zbl 0215.366)].
scientific article; zbMATH DE number 783917