An Exact Sequence Associated with a Generalized Crossed Product

Abstract

The purpose of this paper is to generalize the seven terms exact sequence given by Chase, Harrison and Rosenberg [8]. Our work was motivated by Kanzaki [16] and, of course, [8], [9]. The main theorem holds for any generalized crossed product, which is a more general one than that in Kanzaki [16]. In §1, we define a group P(A/B) for any ring extension A/B, and prove some preliminary exact sequences. In §2, we fix a group homomorphism J from a group G to the group of all invertible two-sided B -submodules of A.