2 citations · 5 across the 9 of their papers we have counts for
9 papers
The algebra of rewriting for presentations of inverse monoids
N. D. Gilbert, E. A. McDougall
We describe a formalism, using groupoids, for the study of rewriting for presentations of inverse monoids, that is based on the Squier complex construction for monoid presentations…
Groupoids and the algebra of rewriting in group presentations
N. D. Gilbert, E. A. McDougall
Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a --complex -- the Squier compl…
The homology of principally directed ordered groupoids
B. O. Bainson, N. D. Gilbert
We present some homological properties of a relation on ordered groupoids that generalises the minimum group congruence for inverse semigroups. When is a transitive relatio…
Cohomology and extensions of ordered groupoids
B. O. Bainson, N. D. Gilbert
We adapt and generalise results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomolog…
Closed inverse subsemigroups of graph inverse semigroups
Amal AlAli, N. D. Gilbert
As part of his study of representations of the polycylic monoids, M.V. Lawson described all the closed inverse submonoids of a polycyclic monoid and classified them up to con…
Inverse subsemigroups of finite index in finitely generated inverse semigroups
Amal AlAli, N. D. Gilbert
The index of a subgroup of a group counts the number of cosets of that subgroup. A subgroup of finite index often shares structural properties with the group, and the existence of…