9 citations · 18 across the 12 of their papers we have counts for
6 papers · 1 filter
F-Inverse Monoids as Weakly Schreier Extensions
Peter F. Faul
It is known that an inverse monoid is E-unitary if and only if the following diagram is an extension: , where is the semilattice of idempotents and $…
The Case for Inverse Semirings
Peter F. Faul, Amartya Goswami, Gideo Joubert +1
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a…
A Survey of Schreier-Type Extensions of Monoids
P. F. Faul
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 gr…
Quotients of monoid extensions and their interplay with Baer sums
Peter Faul, Graham Manuell
Cosetal extensions of monoids generalise extensions of groups, special Schreier extensions of monoids and Leech's normal extensions of groups by monoids. They share a number of pro…
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…
-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…