Decomposition of algebras over \(F_ q(X_ 1,\dots,X_ m)\) (Q1320439)

Let \(A\) be a finite dimensional algebra over a field \(F\) that is a finite extension of the function field \(\mathbb{F}_ q(X_ 1,\dots,X_ m)\) given by its structure constants. The authors show how the Jacobson radical of \(A\) and the decomposition of a semisimple algebra into simple algebras can be computed. The complexity of the algorithms are exponential in \(m\) but polynomial in the other parameters.