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

2020Journal article Open access
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dc.contributor.authorMartins-Ferreira, Nelson
dc.contributor.authorMontoli, Andrea
dc.contributor.authorPatchkoria, Alex
dc.contributor.authorSobral, Manuela
dc.date.accessioned2023-04-17T09:41:54Z
dc.date.available2023-04-17T09:41:54Z
dc.date.issued2020
dc.descriptionThis 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”.pt_PT
dc.description.abstractWe 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)).pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationMartins-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-2019-0164pt_PT
dc.identifier.doi10.1515/forum-2019-0164pt_PT
dc.identifier.issn1435-5337
dc.identifier.urihttp://hdl.handle.net/10400.8/8387
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherDe Gruyterpt_PT
dc.relationCenter for Mathematics, University of Coimbra
dc.relationCentre for Rapid and Sustainable Product Development
dc.relation.publisherversionhttps://www.degruyter.com/document/doi/10.1515/forum-2019-0164/html#APApt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectMonoidpt_PT
dc.subjectSchreier extensionpt_PT
dc.subjectObstructionpt_PT
dc.subjectEilenberg–Mac Lane cohomology of monoidspt_PT
dc.titleOn the classification of Schreier extensions of monoids with non-abelian kernelpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter for Mathematics, University of Coimbra
oaire.awardTitleCentre for Rapid and Sustainable Product Development
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00324%2F2019/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMulti%2F04044%2F2019/PT
oaire.citation.endPage623pt_PT
oaire.citation.issue3pt_PT
oaire.citation.startPage607pt_PT
oaire.citation.titleForum Mathematicumpt_PT
oaire.citation.volume32pt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
person.familyNameMartins-Ferreira
person.givenNameNelson
person.identifier485301
person.identifier.ciencia-idB115-B65E-24AA
person.identifier.orcid0000-0002-4199-7367
person.identifier.ridN-1699-2013
person.identifier.scopus-author-id24598020700
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
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