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<meta content="Easdown, David" name="eprints.creators_name" />
<meta content="East, James" name="eprints.creators_name" />
<meta content="FitzGerald, D.G." name="eprints.creators_name" />
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<meta content="It is well-known that an inverse monoid is factorizable if and only if it is a homomorphic
image of a semidirect product of a semilattice (with identity) by a group.
We use this structure to describe a presentation of an arbitrary factorizable inverse
monoid in terms of presentations of its group of units and semilattice of idempotents,
together with some other data. We apply this theory to quickly deduce a well known
presentation of the symmetric inverse monoid on a nite set." name="eprints.abstract" />
<meta content="2005" name="eprints.date" />
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<meta content="Acta Universitatis Szegediensis, Acta Scientiarum Mathematicarum" name="eprints.publication" />
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<meta content="[1] S. Y. Chen and S. C. Hsieh. Factorizable Inverse Semigroups. Semigroup Forum,
8(4):283-297, 1974.
[2] A. H. Clifford and G. B. Preston. The Algebraic Theory of Semigroups Vol II. Number
7 in Mathematical Surveys. Amer. Math. Soc., Providence, R.I., 1967.
[3] E. Dombi. Almost Factorizable Straight Locally Inverse Semigroups. Acta Sci. Math.
(Szeged), 69(3-4):569-589, 2003.
[4] D. Easdown, J. East, and D. G. FitzGerald. Braids and Factorizable Inverse Monoids.
Semigroups and Languages, eds. I.M. Araujo, M.J.J. Branco, V.H. Fernandes, and
G.M.S. Gomes, World Scientific, pages 86-105, 2002.
[5] D. Easdown and T. G. Lavers. The Inverse Braid Monoid. Adv. Math., 186(2):438-455,
2004.
[6] J. East. The Permeable Braid Monoid. in preparation.
[7] J. East. Cofull Embeddings in Coset Monoids. preprint.
[8] J. East. The Factorizable Braid Monoid. Proc. Edinb. Math. Soc. (2) 49(3):609-636, 2006.
[9] J. East. Factorizable Inverse Monoids of Cosets of Subgroups of Groups. Comm. Alg., 34(7):2659-2665, 2006.
[10] D. G. FitzGerald and J. Leech. Dual Symmetric Inverse Semigroups and Representation
Theory. J. Austral. Math. Soc., 64:146-182, 1998.
[11] T. G. Lavers. Presentations of General Products of Monoids. J. Algebra, 204(2):733-
741, 1998.
[12] M. V. Lawson. Inverse Semigroups. The Theory of Partial Symmetries. World Scientific Publishing Co., Inc., River Edge, NJ, 1998.
[13] S. Lipscombe. Symmetric Inverse Semigroups. American Mathematical Society, Providence,
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[14] D. B. McAlister. Embedding Inverse Semigroups in Coset Semigroups. Semigroup
Forum, 20:255-267, 1980.
[15] R. N. McKenzie, G. F. McNulty, and W. F. Taylor. Algebras, Lattices, and Varieties.
Volume 1. Wadsworth & Brooks/Cole Mathematics Series. Wadsworth & Brooks/Cole
Advanced Books & Software, Monterey, CA, 1987.
[16] John C. Meakin. An Invitation to Inverse Semigroup Theory. Proceedings of the
Conference on Ordered Structures and Algebra of Computer Languages (K. P. Shum
and P. C. Yuen, Eds., World Scientific, Singapore), pages 91-115, 1993.
9
[17] Janet E. Mills. Combinatorially Factorizable Inverse Monoids. Semigroup Forum,
59(2):220-232, 1999.
[18] E. H. Moore. Concerning the Abstract Groups of Order k! and 1/2 k! Holohedrically
Isomorphic with the Symmetric and Alternating Substitution Groups on k Letters.
Proc. London Math. Soc., 28:357{366, 1897.
[19] L. M. Popova. Defining Relations in some Semigroups of Partial Transformations of a
Finite Set (in Russian). Uchenye Zap. Leningrad Gos. Ped. Inst., 218:191-212, 1961.
[20] L. Solomon. Representations of the Rook Monoid. J. Algebra, 256(2):309-342, 2002.
[21] L. Solomon. The Iwahori Algebra of Mn(Fq). A Presentation and a Representation
on Tensor Space. J. Algebra, 273(1):206-226, 2004.
[22] Yupaporn Tirasupa. Factorizable Transformation Semigroups. Semigroup Forum,
18(1):15-19, 1979.
[23] Yupaporn Tirasupa. Weakly Factorizable Inverse Semigroups. Semigroup Forum,
18(4):283-291, 1979.
[24] R. Wilkinson. A Description of E-Unitary Inverse Semigroups. Proc. Roy. Soc. Edinburgh
Sect. A, 95(3-4):239-242, 1983." name="eprints.referencetext" />
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<meta content="It is well-known that an inverse monoid is factorizable if and only if it is a homomorphic
image of a semidirect product of a semilattice (with identity) by a group.
We use this structure to describe a presentation of an arbitrary factorizable inverse
monoid in terms of presentations of its group of units and semilattice of idempotents,
together with some other data. We apply this theory to quickly deduce a well known
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<h1 class="ep_tm_pagetitle">Presentations of factorizable inverse monoids</h1>
<p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Easdown, David</span> and <span class="person_name">East, James</span> and <span class="person_name">FitzGerald, D.G.</span> (2005) <xhtml:em>Presentations of factorizable inverse monoids.</xhtml:em> Acta Universitatis Szegediensis, Acta Scientiarum Mathematicarum, 71 (3-4). pp. 509-520.</p><p style="margin-bottom: 1em" class="not_ep_block"></p><table style="margin-bottom: 1em" class="not_ep_block"><tr><td valign="top" style="text-align:center"><a onmouseover="EPJS_ShowPreview( event, 'doc_preview_1841' );" href="http://eprints.utas.edu.au/1431/1/EEF_PresentationsFactorizable.pdf" onmouseout="EPJS_HidePreview( event, 'doc_preview_1841' );"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" class="ep_doc_icon" border="0" /></a><div class="ep_preview" id="doc_preview_1841"><table><tr><td><img alt="" src="http://eprints.utas.edu.au/1431/thumbnails/1/preview.png" class="ep_preview_image" border="0" /><div class="ep_preview_title">Preview</div></td></tr></table></div></td><td valign="top"><a href="http://eprints.utas.edu.au/1431/1/EEF_PresentationsFactorizable.pdf"><span class="ep_document_citation">PDF (Author Version)</span></a> - Requires a PDF viewer<br />125Kb</td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://www.math.u-szeged.hu/acta/">http://www.math.u-szeged.hu/acta/</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">It is well-known that an inverse monoid is factorizable if and only if it is a homomorphic
image of a semidirect product of a semilattice (with identity) by a group.
We use this structure to describe a presentation of an arbitrary factorizable inverse
monoid in terms of presentations of its group of units and semilattice of idempotents,
together with some other data. We apply this theory to quickly deduce a well known
presentation of the symmetric inverse monoid on a nite set.</p></div><table style="margin-bottom: 1em" cellpadding="3" class="not_ep_block" border="0"><tr><th valign="top" class="ep_row">Item Type:</th><td valign="top" class="ep_row">Article</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">Factorizable inverse monoid, presentations, symmetric inverse monoid</td></tr><tr><th valign="top" class="ep_row">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/230105.html">230000 Mathematical Sciences > 230100 Mathematics > 230105 Group Theory And Generalisations (Incl. Topological Groups And Lie Groups)</a></td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">1431</td></tr><tr><th valign="top" class="ep_row">Deposited By:</th><td valign="top" class="ep_row"><span class="ep_name_citation"><span class="person_name">Dr D. G. FitzGerald</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">23 Aug 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">09 Jan 2008 02:30</td></tr><tr><th valign="top" class="ep_row">ePrint Statistics:</th><td valign="top" class="ep_row"><a target="ePrintStats" href="/es/index.php?action=show_detail_eprint;id=1431;">View statistics for this ePrint</a></td></tr></table><p align="right">Repository Staff Only: <a href="http://eprints.utas.edu.au/cgi/users/home?screen=EPrint::View&eprintid=1431">item control page</a></p>
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