Invertible unital bimodules over rings with local units, and related exact sequences of groups II

Details Invertible unital bimodules over rings with local units, and related exact sequences of groups II Invertible unital bimodules over rings with local units, and related exact sequences of groups II

2011-09-23

arxiv.org/abs/1109.5062v1

Mathematics

Rings and Algebras

Scientific paper

Let $R$ be a ring with a set of local units, and a homomorphism of groups $\underline{\Theta} : \G \to \Picar{R}$ to the Picard group of $R$. We study under which conditions $\underline{\Theta}$ is determined by a factor map, and, henceforth, it defines a generalized crossed product with a same set of local units. Given a ring extension $R \subseteq S$ with the same set of local units and assuming that $\underline{\Theta}$ is induced by a homomorphism of groups $\G \to \Inv{R}{S}$ to the group of all invertible $R$-sub-bimodules of $S$, then we construct an analogue of the Chase-Harrison-Rosenberg seven terms exact sequence of groups attached to the triple $(R \subseteq S, \underline{\Theta})$, which involves the first, the second and the third cohomology groups of $\G$ with coefficients in the group of all $R$-bilinear automorphisms of $R$. Our approach generalizes the works by Kanzaki and Miyashita in the unital case.

Affiliated with

Also associated with

No associations

Rating

Invertible unital bimodules over rings with local units, and related exact sequences of groups II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Invertible unital bimodules over rings with local units, and related exact sequences of groups II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invertible unital bimodules over rings with local units, and related exact sequences of groups II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-724233