Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/89460
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dc.contributor.authorMartins-Ferreira, Nelson-
dc.contributor.authorMontoli, Andrea-
dc.contributor.authorPatchkoria, Alex-
dc.contributor.authorSobral, Manuela-
dc.date.accessioned2020-06-04T14:44:58Z-
dc.date.available2020-06-04T14:44:58Z-
dc.date.issued2020-
dc.identifier.urihttp://hdl.handle.net/10316/89460-
dc.description.abstractWe show that any regular (right) Schreier extension of a monoid M by a monoid A induces an abstract kernel \Phi: M \rightarrow\frac{End(A)}{Inn(A)}. If an abstract kernel factors through \frac{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 coeffcients in the abelian group U(Z(A)) of invertible elements of the center Z(A) of A, on which M acts via \Phi. An abstract kernel \Phi: M \rightarrow\frac{SEnd(A)}{Inn(A)} (resp. \Phi: M \rightarrow\frac{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 \Phi: M \rightarrow\frac{SEnd(A)}{Inn(A)} (resp. \Phi: M \rightarrow\frac{Aut(A)}{Inn(A)}), when it is not empty, is in bijection with the second cohomology group of M with coeffcients in U(Z(A)).pt
dc.language.isoengpt
dc.publisherDe Gruyterpt
dc.relationUID/MAT/00324/2019pt
dc.rightsembargoedAccesspt
dc.subjectMonoid; Schreier extension; obstruction; Eilenberg–Mac Lane cohomology of monoidspt
dc.titleOn the classification of Schreier extensions of monoids with non-abelian kernelpt
dc.typearticle-
degois.publication.issue3pt
degois.publication.titleForum Mathematicumpt
dc.relation.publisherversionhttps://www.degruyter.com/view/journals/form/32/3/article-p607.xmlpt
dc.peerreviewedyespt
dc.identifier.doi10.1515/forum-2019-0164pt
degois.publication.volume32pt
dc.date.embargo2020-12-31*
uc.date.periodoEmbargo365pt
item.fulltextCom Texto completo-
item.languageiso639-1en-
item.grantfulltextopen-
crisitem.author.deptFaculty of Sciences and Technology-
crisitem.author.parentdeptUniversity of Coimbra-
crisitem.author.researchunitCMUC - Centre for Mathematics of the University of Coimbra-
crisitem.author.orcid0000-0001-9289-6147-
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais
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