Ordered groupoids and the holomorph of an inverse semigroup

N. D. Gilbert; E. A. McDougall

doi:10.1007/s00233-014-9670-4

Ordered groupoids and the holomorph of an inverse semigroup

N. D. Gilbert^*, E. A. McDougall

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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 inverse semigroup: for groups these two constructions coincide. We present detailed calculations for semilattices of groups and for the polycyclic monoids.

Original language	English
Pages (from-to)	648-662
Number of pages	15
Journal	Semigroup Forum
Volume	91
Issue number	3
Early online date	11 Dec 2014
DOIs	https://doi.org/10.1007/s00233-014-9670-4
Publication status	Published - Dec 2015

Keywords

Endomorphism
Holomorph
Inverse semigroup
Ordered groupoid

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s00233-014-9670-4

Cite this

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title = "Ordered groupoids and the holomorph of an inverse semigroup",

abstract = "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 inverse semigroup: for groups these two constructions coincide. We present detailed calculations for semilattices of groups and for the polycyclic monoids.",

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AU - Gilbert, N. D.

AU - McDougall, E. A.

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AB - 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 inverse semigroup: for groups these two constructions coincide. We present detailed calculations for semilattices of groups and for the polycyclic monoids.

KW - Endomorphism

KW - Holomorph

KW - Inverse semigroup

KW - Ordered groupoid

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U2 - 10.1007/s00233-014-9670-4

DO - 10.1007/s00233-014-9670-4

M3 - Article

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EP - 662

JO - Semigroup Forum

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ER -

Ordered groupoids and the holomorph of an inverse semigroup

Abstract

Keywords

ASJC Scopus subject areas

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