| Full text | |
| Author(s): |
Dokuchaev, Mikhailo
;
Rocha, Itailma
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Pure and Applied Algebra; v. 228, n. 5, p. 62-pg., 2023-11-13. |
| Abstract | |
Given a non-necessarily commutative unital ring R and a unital partial representation Theta of a group G into the Picard semigroup PicS(R) of the isomorphism classes of partially invertible R-bimodules, we construct an abelian group C(Theta/R) formed by the isomorphism classes of partial generalized crossed products related to Theta and identify an appropriate second partial cohomology group of G with a naturally defined subgroup C0(Theta/R) of C(Theta/R). Then we use the obtained results to give an analogue of the Chase-Harrison-Rosenberg exact sequence associated with an extension of non-necessarily commutative rings R subset of S with the same unity and a unital partial representation G -> SR(S) of an arbitrary group G into the monoid SR(S) of the R-subbimodules of S. This generalizes the works by Kanzaki and Miyashita. (c) 2023 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 20/16594-0 - Non commutative rings and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |