2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137518We show a tensorial-computational way to find out conditions that must fulfil an m-rank tensor in arbitrary dimension in order to be algebraically the energy-momentum tensor of some field. We apply in this paper our method to three 2-rank tensors: electromagnetic, mass less scalar field and perfect fluid tensors. Finally we apply the Rainich theory to some examples.7 pages, submitted to GRGGeneral Relativity and Quantum Cosmologytext