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arXiv · 1109.5062

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

L. EL Kaoutit·J. Gómez-Torrecillas
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Abstract

Let $R$ be a ring with a set of local units, and a homomorphism of groups $\underlineΘ : \G \to \Picar{R}$ to the Picard group of $R$. We study under which conditions $\underlineΘ$ 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 $\underlineΘ$ 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 $(R \subseteq S, \underlineΘ)$, 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.

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L. EL Kaoutit, J. Gómez-Torrecillas. 2011-09-23. Invertible unital bimodules over rings with local units, and related exact sequences of groups II. https://arxiv.org/abs/1109.5062

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