2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112835A wide generalization of the classical theorem of A. Grothendieck asserting that for any faithfully flat extension of commutative rings, the corresponding relative Picard group and the Amitsur 1-cohomology group with values in the units-functor are isomorphic, is obtained. This implies some known results that are concerned with extending to non-commutative rings of Grothendieck's theorem.Rings and Algebras16W30; 18C15text