2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141903In this paper, first we give a simple criterion for the Arens regularity of a bilinear mapping on normed spaces, which applies in particular to Banach module actions and then we investigate those conditions under which the second adjoint of a derivation into a dual Banach module is again a derivation. As a consequence of the main result, a simple and direct proof for several older results is also included.15 pages. To appear in Bull. Austral. Math. SocFunctional Analysis46H20; 46H25text