Partial generalized crossed products and a seven term exact sequence.

Given a non-necessarily commutative unital ring R and a unital partial representation Θ of a group G into the Picard semigroup PicS (R) of the isomorphism classes of partially invertible R -bimodules, we construct an abelian group C (Θ / R) formed by the isomorphism classes of partial generalized crossed products related to Θ and identify an appropriate second partial cohomology group of G with a naturally defined subgroup C 0 (Θ / R) of C (Θ / R). Then we use the obtained results to give an analogue of the Chase-Harrison-Rosenberg exact sequence associated with an extension of non-necessarily commutative rings R ⊆ S with the same unity and a unital partial representation G → S R (S) of an arbitrary group G into the monoid S R (S) of the R -subbimodules of S. This generalizes the works by Kanzaki and Miyashita. [ABSTRACT FROM AUTHOR]