P. Faul

activity

20192025

collaborators

5 papers

math.RA2025

F-Inverse Monoids as Weakly Schreier Extensions

Peter F. Faul

It is known that an inverse monoid $M$ is E-unitary if and only if the following diagram is an extension: $E (M) \to M \to M / σ$ , where $E (M)$ is the semilattice of idempotents and $…

math.GR2024

The Reverse Representation Problem

Peter F. Faul, Zurab Janelideze, Gideo Joubert

Cayley's theorem tells us that all groups $G$ occur as subgroups of the group of automorphisms over some set $X$ . In this paper we consider a `sort-of' converse to this qu…

math.RA2020

Baer sums for a natural class of monoid extensions

Peter Faul

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 c…

math.RA2020

$λ$ -Semidirect Products of Inverse Monoids are Weakly Schreier Extensions

Peter Faul

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…

math.CT2019

A characterization of weakly Schreier extensions of monoids

P. F. Faul

A split extension of monoids with kernel $k : N \to G$ , cokernel $e : G \to H$ and splitting $s : H \to G$ is Schreier if there exists a unique set-theoretic map $q…