On the classification of Schreier extensions of monoids with non-abelian kernel

Detalhes bibliográficos
Autor(a) principal: Martins-Ferreira, Nelson
Data de Publicação: 2020
Outros Autores: Montoli, Andrea, Patchkoria, Alex, Sobral, Manuela
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.8/8387
Resumo: This work was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2019, by ESTG and CDRSP from the Polytechnical Institute of Leiria – UID/Multi/04044/ 2019, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020. The second author was partially supported by the Programma per Giovani Ricercatori “Rita Levi-Montalcini”, funded by the Italian government through MIUR. The third author was supported by the Shota Rustaveli National Science Foundation of Georgia (SRNSFG), grant FR-18-10849, “Stable Structures in Homological Algebra”.
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spelling On the classification of Schreier extensions of monoids with non-abelian kernelMonoidSchreier extensionObstructionEilenberg–Mac Lane cohomology of monoidsThis work was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2019, by ESTG and CDRSP from the Polytechnical Institute of Leiria – UID/Multi/04044/ 2019, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020. The second author was partially supported by the Programma per Giovani Ricercatori “Rita Levi-Montalcini”, funded by the Italian government through MIUR. The third author was supported by the Shota Rustaveli National Science Foundation of Georgia (SRNSFG), grant FR-18-10849, “Stable Structures in Homological Algebra”.We show that any regular (right) Schreier extension of a monoid M by a monoid A induces an abstract kernel Φ: M → End(A)/Inn(A) . If an abstract kernel factors through SEnd(A)/Inn(A) , where SEnd(A) is the monoid of surjective endomorphisms of A, then we associate to it an obstruction, which is an element of the third cohomology group of M with coefficients in the abelian group U(Z(A)) of invertible elements of the center Z(A) of A, on which M acts via Φ. An abstract kernel Φ: M → SEnd(A)/Inn(A) (resp. Φ: M → Aut(A)/Inn(A) ) is induced by a regular weakly homogeneous (resp. homogeneous) Schreier extension of M by A if and only if its obstruction is zero.We also show that the set of isomorphism classes of regular weakly homogeneous (resp. homogeneous) Schreier extensions inducing a given abstract kernel Φ: M → SEnd(A)/Inn(A) (resp. Φ: M → Aut(A)/Inn(A) ), when it is not empty, is in bijection with the second cohomology group of M with coefficients in U(Z(A)).De GruyterIC-OnlineMartins-Ferreira, NelsonMontoli, AndreaPatchkoria, AlexSobral, Manuela2023-04-17T09:41:54Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/8387engMartins-Ferreira, N., Montoli, A., Patchkoria, A. & Sobral, M. (2020). On the classification of Schreier extensions of monoids with non-abelian kernel. Forum Mathematicum, 32(3), 607-623. https://doi.org/10.1515/forum-2019-01641435-533710.1515/forum-2019-0164info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-17T15:57:13Zoai:iconline.ipleiria.pt:10400.8/8387Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:51:07.319603Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On the classification of Schreier extensions of monoids with non-abelian kernel
title On the classification of Schreier extensions of monoids with non-abelian kernel
spellingShingle On the classification of Schreier extensions of monoids with non-abelian kernel
Martins-Ferreira, Nelson
Monoid
Schreier extension
Obstruction
Eilenberg–Mac Lane cohomology of monoids
title_short On the classification of Schreier extensions of monoids with non-abelian kernel
title_full On the classification of Schreier extensions of monoids with non-abelian kernel
title_fullStr On the classification of Schreier extensions of monoids with non-abelian kernel
title_full_unstemmed On the classification of Schreier extensions of monoids with non-abelian kernel
title_sort On the classification of Schreier extensions of monoids with non-abelian kernel
author Martins-Ferreira, Nelson
author_facet Martins-Ferreira, Nelson
Montoli, Andrea
Patchkoria, Alex
Sobral, Manuela
author_role author
author2 Montoli, Andrea
Patchkoria, Alex
Sobral, Manuela
author2_role author
author
author
dc.contributor.none.fl_str_mv IC-Online
dc.contributor.author.fl_str_mv Martins-Ferreira, Nelson
Montoli, Andrea
Patchkoria, Alex
Sobral, Manuela
dc.subject.por.fl_str_mv Monoid
Schreier extension
Obstruction
Eilenberg–Mac Lane cohomology of monoids
topic Monoid
Schreier extension
Obstruction
Eilenberg–Mac Lane cohomology of monoids
description This work was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2019, by ESTG and CDRSP from the Polytechnical Institute of Leiria – UID/Multi/04044/ 2019, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020. The second author was partially supported by the Programma per Giovani Ricercatori “Rita Levi-Montalcini”, funded by the Italian government through MIUR. The third author was supported by the Shota Rustaveli National Science Foundation of Georgia (SRNSFG), grant FR-18-10849, “Stable Structures in Homological Algebra”.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
2023-04-17T09:41:54Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.8/8387
url http://hdl.handle.net/10400.8/8387
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Martins-Ferreira, N., Montoli, A., Patchkoria, A. & Sobral, M. (2020). On the classification of Schreier extensions of monoids with non-abelian kernel. Forum Mathematicum, 32(3), 607-623. https://doi.org/10.1515/forum-2019-0164
1435-5337
10.1515/forum-2019-0164
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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