Diagonalizability of traces (Q1196813)

For any finite-dimensional algebra \(A\) over a field \(F\) is shown that the bilinear forms associated with the characters of the left and right regular representations of \(A\) can be simultaneously diagonalized. The section of results contains three propositions and two theorems. The results of Theorem 4 in the paper can be extended to a slightly more general context. Take \(A\) to be a ring, finitely generated over a central subring \(R\), where \(R\) is noetherian and regular; then using the Hattori- Stallings trace and a suitable localization one gets a result analogous to Theorem 4.