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pro vyhledávání: '"Nicholas David Gilbert"'
Autor:
E.A.McDougall, Nicholas David Gilbert
Publikováno v:
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 62:623-639
Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a 2-complex—the Squier complex—whose fundamental groupoid then describes the derivation of consequen
Autor:
E.A.McDougall, Nicholas David Gilbert
Publikováno v:
Communications in Algebra. 48:2920-2940
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. We introduce th...
Publikováno v:
Homology, Homotopy and Applications. 22:163-172
We present some homological properties of a relation $\beta$ on ordered groupoids that generalises the minimum group congruence for inverse semigroups. When $\beta$ is a transitive relation on an ordered groupoid $G$, the quotient $G / \beta$ is agai
Publikováno v:
Journal of Algebra and Its Applications. 21
We adapt and generalize results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this sequence
Autor:
Nicholas David Gilbert, Nouf AlYamani
Publikováno v:
Semigroup Forum. 96:506-522
We introduce a preorder on an inverse semigroup S associated to any normal inverse subsemigroup N, that lies between the natural partial order and Green’s $${\mathcal {J}}$$ –relation. The corresponding equivalence relation $$\simeq _N$$ is not n
Publikováno v:
Semigroup Forum. 96:489-505
We study some aspects of Schein’s theory of cosets for closed inverse subsemigroups of inverse semigroups. We establish an index formula for chains of subsemigroups, and an analogue of M. Hall’s Theorem on the number of cosets of a fixed finite i
Autor:
Nicholas David Gilbert
Publikováno v:
Archiv der Mathematik. 108:365-371
A labelled oriented graph (LOG) group is a group given by a presentation constructed in a certain way from a labelled oriented graph: examples include Wirtinger presentations of knot groups. We show how to obtain generators for the Schur Multiplier $
Publikováno v:
Communications in Algebra. 45:4667-4678
As part of his study of representations of the polycylic monoids, Lawson described all the closed inverse submonoids of a polycyclic monoid Pn and classified them up to conjugacy. We show that Lawson’s description can be extended to closed inverse
Publikováno v:
Applied Categorical Structures. 24:121-146
We investigate canonical factorizations of ordered functors of ordered groupoids through star-surjective functors. Our main construction is a quotient ordered groupoid, depending on an ordered version of the notion of normal subgroupoid, that results
Autor:
Nicholas David Gilbert, E.A.McDougall
Publikováno v:
Semigroup Forum. 91:648-662
We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap operation on an