Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invertible unital bimodules over rings with local units, and related
  exact sequences of groups II   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.

23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con