Finding the radical of matrix algebras using Fitting decompositions Original Research Article

We present a new approach to calculating the radical of a matrix algebra, based on the Fitting decomposition with respect to the simultaneous adjoint action of certain commutative subalgebras. This idea results in a reduction to finding the radical of a Lie nilpotent subalgebra or a commutative factor thereof. We also describe a probabilistic version for computing elements which generate the radical as an ideal.