Journal
JOURNAL OF ALGEBRA
Volume 370, Issue -, Pages 266-296Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jalgebra.2012.07.035
Keywords
Rings with local units; Unital bimodules; Picard groups; Brauer groups
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Funding
- Ministerio de Ciencia e Innovacion [MTM2010-20940-C02-01]
- FEDER
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Let R be a ring with a set of local units, and a homomorphism of groups (Theta) under bar : G -> Pic(R) to the Picard group of R. We study under which conditions (Theta) under bar 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 subset of S with the same set of local units and assuming that (Theta) under bar is induced by a homomorphism of groups G -> 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 subset of S, (Theta) under bar), 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. (C) 2012 Elsevier Inc. All rights reserved.
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