Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/89460
 Title: On the classification of Schreier extensions of monoids with non-abelian kernel Authors: Martins-Ferreira, NelsonMontoli, AndreaPatchkoria, AlexSobral, Manuela Keywords: Monoid; Schreier extension; obstruction; Eilenberg–Mac Lane cohomology of monoids Issue Date: 2020 Publisher: De Gruyter Project: UID/MAT/00324/2019 Serial title, monograph or event: Forum Mathematicum Volume: 32 Issue: 3 Abstract: We 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)). URI: http://hdl.handle.net/10316/89460 DOI: 10.1515/forum-2019-0164 Rights: embargoedAccess Appears in Collections: I&D CMUC - Artigos em Revistas Internacionais

###### Files in This Item:
non ab monoid ext 7.pdf338.91 kBAdobe PDFEmbargo Access

#### Page view(s)

5
checked on Jul 9, 2020

2
checked on Jul 9, 2020