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Partial generalized crossed products and a seven term exact sequence

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Autor(es):
Dokuchaev, Mikhailo ; Rocha, Itailma
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: Journal of Pure and Applied Algebra; v. 228, n. 5, p. 62-pg., 2023-11-13.
Resumo

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)

Processo FAPESP: 20/16594-0 - Anéis não comutativos e aplicações
Beneficiário:Francisco Cesar Polcino Milies
Modalidade de apoio: Auxílio à Pesquisa - Temático