NONLINEAR MAPPINGS WHOSE JACOBI MATRIX COMMUTES WITH CONSTANT MATRICES OF A RING

摘要

We obtain a criterion for the existence of a nonlinear mapping u : C~m → C~m (m ≥ 2) whose Jacobi matrix commutes with each constant complex matrix of a given ring Q. We show that such a mapping exists if and only if the ring Q has at least one (r, l)-pair.