Representation Theory of Semigroups

Lead Research Organisation: University of St Andrews
Department Name: Mathematics and Statistics

Abstract

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Publications

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Abu-Ghazalh N (2014) A classification of disjoint unions of two or three copies of the free monogenic semigroup in Semigroup Forum

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Abu-Ghazalh N (2013) On disjoint unions of finitely many copies of the free monogenic semigroup in Semigroup Forum

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Craik S (2016) Ends of semigroups in Semigroup Forum

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DOLINKA I (2013) EVERY GROUP IS A MAXIMAL SUBGROUP OF THE FREE IDEMPOTENT GENERATED SEMIGROUP OVER A BAND in International Journal of Algebra and Computation

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Dolinka I (2017) On regularity and the word problem for free idempotent generated semigroups THE WORD PROBLEM FOR FREE IDEMPOTENT GENERATED SEMIGROUPS in Proceedings of the London Mathematical Society

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Gould V (2016) Free Monoids are Coherent in Proceedings of the Edinburgh Mathematical Society

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GRAY R (2013) IDEALS AND FINITENESS CONDITIONS FOR SUBSEMIGROUPS in Glasgow Mathematical Journal

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Gray R (2012) Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid in Proceedings of the London Mathematical Society

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Gray R (2011) On maximal subgroups of free idempotent generated semigroups in Israel Journal of Mathematics

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Gray R (2014) On residual finiteness of monoids, their Schützenberger groups and associated actions in Journal of Algebra

 
Description Representations of semigroups of different types have been investigated. Major progress has been achieved in the study of free idempotent generated semigroups has been achieved, where a number of open problems has been resolved. Further representations related to automata/languages, as well as to semigroup structure theory, have been studied.
Exploitation Route The result of this project have initiated further research in the areas of free idempotent generated semigroups and automaton semigroups.
Sectors Digital/Communication/Information Technologies (including Software)