ROS Theses Repository

View Item 
  •   ROS Home
  • Mathematical & Computer Sciences
  • Doctoral Theses (Mathematical & Computer Sciences)
  • View Item
  •   ROS Home
  • Mathematical & Computer Sciences
  • Doctoral Theses (Mathematical & Computer Sciences)
  • View Item
  •   ROS Home
  • Mathematical & Computer Sciences
  • Doctoral Theses (Mathematical & Computer Sciences)
  • View Item
  • Admin
JavaScript is disabled for your browser. Some features of this site may not work without it.

Graph expansions of semigroups

View/Open
HealeRN_0510_macs.pdf (1.792Mb)
Date
2010-05
Author
Heale, Rebecca Noonan
Metadata
Show full item record
Abstract
We construct a graph expansion from a semigroup with a given generating set, thereby generalizing the graph expansion for groups introduced by Margolis and Meakin. We then describe structural properties of this expansion. The semigroup graph expansion is itself a semigroup and there is a map onto the original semigroup. This construction preserves many features of the original semigroup including the presence of idempotent/periodic elements, maximal group images (if the initial semigroup is E-dense), finiteness, and finite subgroup structure. We provide necessary and sufficient graphical criteria to determine if elements are idempotent, regular, periodic, or related by Green’s relations. We also examine the relationship between the semigroup graph expansion and other expansions, namely the Birget and Rhodes right prefix expansion and the monoid graph expansion. If S is a -generated semigroup, its graph expansion is generally not -generated. For this reason, we introduce a second construction, the path expansion of a semigroup. We show that it is a -generated subsemigroup of the semigroup graph expansion. The semigroup path expansion possesses most of the properties of the semigroup graph expansion. Additionally, we show that the path expansion construction plays an analogous role with respect to the right prefix expansion of semigroups that the group graph expansion plays with respect to the right prefix expansion of groups.
URI
http://hdl.handle.net/10399/2391
Collections
  • Doctoral Theses (Mathematical & Computer Sciences)

Browse

All of ROSCommunities & CollectionsBy Issue DateAuthorsTitlesThis CollectionBy Issue DateAuthorsTitles

ROS Administrator

LoginRegister
©Heriot-Watt University, Edinburgh, Scotland, UK EH14 4AS.

Maintained by the Library
Tel: +44 (0)131 451 3577
Library Email: libhelp@hw.ac.uk
ROS Email: open.access@hw.ac.uk

Scottish registered charity number: SC000278

  • About
  • Copyright
  • Accessibility
  • Policies
  • Privacy & Cookies
  • Feedback
AboutCopyright
AccessibilityPolicies
Privacy & Cookies
Feedback
 
©Heriot-Watt University, Edinburgh, Scotland, UK EH14 4AS.

Maintained by the Library
Tel: +44 (0)131 451 3577
Library Email: libhelp@hw.ac.uk
ROS Email: open.access@hw.ac.uk

Scottish registered charity number: SC000278

  • About
  • Copyright
  • Accessibility
  • Policies
  • Privacy & Cookies
  • Feedback
AboutCopyright
AccessibilityPolicies
Privacy & Cookies
Feedback