  A 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.
