2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159008We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of pull-back morphisms and of base-preserving morphisms associated to Lie algebroid extensions. We also define generalized morphisms, including Morita equivalences, that act on the 1-cohomology, and observe that the relative modular class is a coboundary on the category of Lie algebroids and generalized morphisms with values in the 1-cohomology.33 pages. Dedicated to Bertram Kostant for his eightieth birthday. Minor changes in version 2: Proposition 3.11 added, typos corectedDifferential GeometrySymplectic Geometry17B99, 53D17text