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dc.contributor.advisorRuškuc, Nik
dc.contributor.authorAbu-Ghazalh, Nabilah Hani
dc.coverage.spatial152en_US
dc.date.accessioned2013-06-13T10:23:41Z
dc.date.available2013-06-13T10:23:41Z
dc.date.issued2013-06-28
dc.identifier.urihttps://hdl.handle.net/10023/3687
dc.description.abstractIn this thesis we prove the following: The semigroup which is a disjoint union of two or three copies of a group is a Clifford semigroup, Rees matrix semigroup or a combination between a Rees matrix semigroup and a group. Furthermore, the semigroup which is a disjoint union of finitely many copies of a finitely presented (residually finite) group is finitely presented (residually finite) semigroup. The constructions of the semigroup which is a disjoint union of two copies of the free monogenic semigroup are parallel to the constructions of the semigroup which is a disjoint union of two copies of a group, i.e. such a semigroup is Clifford (strong semilattice of groups) or Rees matrix semigroup. However, the semigroup which is a disjoint union of three copies of the free monogenic semigroup is not just a strong semillatice of semigroups, Rees matrix semigroup or combination between a Rees matrix semigroup and a semigroup, but there are two more semigroups which do not arise from the constructions of the semigroup which is a disjoint union of three copies of a group. We also classify semigroups which are disjoint unions of two or three copies of the free monogenic semigroup. There are three types of semigroups which are unions of two copies of the free monogenic semigroup and nine types of semigroups which are unions of three copies of the free monogenic semigroup. For each type of such semigroups we exhibit a presentation defining semigroups of this type. The semigroup which is a disjoint union of finitely many copies of the free monogenic semigroup is finitely presented, residually finite, hopfian, has soluble word problem and has soluble subsemigroup membership problem.en_US
dc.language.isoenen_US
dc.publisherUniversity of St Andrews
dc.rightsCreative Commons Attribution 3.0 Unported
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/
dc.subjectFree monogenic semigroupen_US
dc.subjectDisjoint unionsen_US
dc.subjectCopiesen_US
dc.subjectClifforden_US
dc.subjectRees matrixen_US
dc.subjectFiniteness conditionsen_US
dc.subjectFinitely presenteden_US
dc.subjectResidually finiteen_US
dc.subjectWord problemen_US
dc.subjectMembership problemen_US
dc.subject.lccQA182.A3
dc.subject.lcshSemigroupsen_US
dc.titleFiniteness conditions for unions of semigroupsen_US
dc.typeThesisen_US
dc.contributor.sponsorPrincess Nora Universityen_US
dc.type.qualificationlevelDoctoralen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US


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Creative Commons Attribution 3.0 Unported
Except where otherwise noted within the work, this item's licence for re-use is described as Creative Commons Attribution 3.0 Unported