I have an algebra $A$ that is finite over its centre $Z(A)$ and I want to compute the Azumaya locus of $Z(A)$ (or equivalently, its ramification locus).
Looking in McConnell-Robson Noncommutative Noetherian rings (13.7.2 together with the Artin-Procesi theorem, 13.7.14) gives some criterium that can be used. However, this seems rather difficult since it means computing PI-degrees or the central polynomial $g_n$ which seems to me quite complicated.
Are there any other, easy ways to compute the Azumaya locus?
As should be clear by the question, I'm very far from an expert in this area, so the question might be very naive or elementary.
