Quotients of monoid extensions and their interplay with Baer sums

  title={Quotients of monoid extensions and their interplay with Baer sums},
  author={P. F. Faul and Graham Manuell},
  journal={Journal of Algebra},

A survey of Schreier-type extensions of monoids

  • P. Faul
  • Mathematics
    Semigroup Forum
  • 2022
We give an overview of a number of Schreier-type extensions of monoids and discuss the relation between them. We begin by discussing the characterisations of split extensions of groups, extensions of

Monoid extensions and the Grothendieck construction

In category theory circles it is well-known that the Schreier theory of group extensions can be understood in terms of the Grothendieck construction on indexed categories. However, it is seldom



Baer sums of special Schreier extensions of monoids

We show that the special Schreier extensions of monoids, with abelian kernel, admit a Baer sum construction, which generalizes the classical one for group extensions with abelian kernel. In order to

Extending Groups by Monoids

Baer sums for a natural class of monoid extensions

  • P. Faul
  • Mathematics
    Semigroup Forum
  • 2021
It is well known that the set of isomorphism classes of extensions of groups with abelian kernel is characterized by the second cohomology group. In this paper we generalise this characterization of

$$\lambda $$-Semidirect products of inverse monoids are weakly Schreier extensions

A split extension of monoids with kernel k: N -> G, cokernel e: G -> H and splitting s: H -> G is weakly Schreier if each element g in G can be written g = k(n)se(g) for some n in N. The

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We investigate the notion of pointed S-protomodular category, with respect to a suitable class S of split epimorphisms, and we prove that these categories satisfy, relatively to the class S, many

Monoid extension theory

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Let B denote a compact semigroup with identity and G a compact abelian group. Let Ext (B, G) denote the semigroup of extensions of G by B. We show that Ext (B, G) is always a union of groups. We show