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<meta content="Gardner, B.J." name="eprints.creators_name" />
<meta content="Parmenter, M.M." name="eprints.creators_name" />
<meta content="Barry.Gardner@utas.edu.au" name="eprints.creators_id" />
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<meta content="2007-08-27" name="eprints.datestamp" />
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<meta content="Directoid groups" name="eprints.title" />
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<meta content="Keywords: directed abelian group, variety.
MSC 2000: 06F20, 08B99" name="eprints.keywords" />
<meta content="Authors' addresses:
B.J.Gardner, Discipline of Mathematics, University of
Tasmania, Private Bag 37, Hobart, Tas. 7001 Australia. gardner@hilbert.maths.utas.edu.au;
M.M.Parmenter, Department of Mathematics and Statistics, Memorial University
of Newfoundland, St John's, NL A1C 5S7 Canada. mparmen@morgan.ucs.mun.ca" name="eprints.note" />
<meta content="We continue the study of directoid groups, directed abelian
groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined
substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups" name="eprints.abstract" />
<meta content="2007-03-22" name="eprints.date" />
<meta content="submitted" name="eprints.date_type" />
<meta content="Czechoslovak Mathematical Journal" name="eprints.publication" />
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<meta content="[1] A.Bigard, K. Keimel and S.Wolfenstein, Groupes et anneaux rÃÂÃÂÃÂéticulÃÂÃÂÃÂés,
Berlin etc., Springer, 1977. Zbl 0619.90014
[2] L.Fuchs, Absolutes in partially ordered groups, Kon. Nederl. Akad.
Wetensch. Proc. Amsterdam 52(1949), 251-255. Zbl 0033.10002
16
[3] L.Fuchs, Partially ordered algebraic systems, Oxford-London-New York-
Paris, Pergamon Press, 1963. Zbl 0137.02001
[4] B.J.Gardner and M.M.Parmenter, Directoids and directed groups, Algebra
Univ. 33(1995), 254-273. Zbl 0832.06005
[5] T.E.Hall, Identities for existence varieties of regular semigroups, Bull.
Austral. Math. Soc. 40(1989), 59-77. Zbl 0666.20028
[6] P.J.Higgins, Groups with multiple operators, Proc. London Math. Soc.
6(1956), 366-416. Zbl 0073.01704
[7] P.Jaard, Un contre-exemple concernant les groupes de divisibilitÃÂÃÂÃÂé, C.R.
Acad. Sci. Paris 243(1956), 1264-1266. Zbl 0071.25405
[8] J.JakubÃÂÃÂÃÂÃÂk, On directed groups with additional operations, Math. Bohemica
118(1993), 11-17. Zbl 0799.06027
[9] J.JeÃÂÃÂÃÂúek and R.Quackenbush, Directoids: algebraic models of up-directed
sets, Algebra Univ. 27(1990), 49-69. Zbl 0699.08002
[10] V.M.Kopytov and Z.I.Dimitrov, On directed groups, Siberian Math. J.
30(1989), 895-902. Zbl 0714.06007
[11] A.G.Kurosh, Lectures on general algebra, New York, Chelsea, 1963. Zbl
0123. 00101
[12] K.Leutola and J. Nieminen, Posets and generalized lattices, Algebra
Univ. 16(1983), 344-354. Zbl 0514.06003
[13] D.B.McAlister, On multilattice groups, Proc. Cambridge Phil. Soc.
61(1965), 621-638. Zbl 0135.06203
[14] J.Nieminen, On distributive and modular -lattices, Yokohama Math.
J. 31(1983), 13-20. Zbl.0532.06002
[15] V. SnÃÂÃÂÃÂáÃÂÃÂÃÂòel, -lattices, Math. Bohemica 122(1997), 267-272. Zbl
0897.06003" name="eprints.referencetext" />
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substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups" name="DC.description" />
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<h1 class="ep_tm_pagetitle">Directoid groups</h1>
<p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Gardner, B.J.</span> and <span class="person_name">Parmenter, M.M.</span> (2007) <xhtml:em>Directoid groups.</xhtml:em> Czechoslovak Mathematical Journal . ISSN 1572-9141 (In Press)</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 href="http://eprints.utas.edu.au/1679/1/dg.pdf"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" border="0" class="ep_doc_icon" /></a></td><td valign="top"><a href="http://eprints.utas.edu.au/1679/1/dg.pdf"><span class="ep_document_citation">PDF</span></a> - Full text restricted - Requires a PDF viewer<br />171Kb</td><td><form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/request_doc"><input value="2168" name="docid" accept-charset="utf-8" type="hidden" /><div class=""><input value="Request a copy" name="_action_null" class="ep_form_action_button" onclick="return EPJS_button_pushed( '_action_null' )" type="submit" /> </div></form></td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://www.springerlink.com">http://www.springerlink.com</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">We continue the study of directoid groups, directed abelian
groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined
substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups</p></div><table style="margin-bottom: 1em" border="0" cellpadding="3" class="not_ep_block"><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">Additional Information:</th><td valign="top" class="ep_row">Authors' addresses:
B.J.Gardner, Discipline of Mathematics, University of
Tasmania, Private Bag 37, Hobart, Tas. 7001 Australia. gardner@hilbert.maths.utas.edu.au;
M.M.Parmenter, Department of Mathematics and Statistics, Memorial University
of Newfoundland, St John's, NL A1C 5S7 Canada. mparmen@morgan.ucs.mun.ca</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">Keywords: directed abelian group, variety.
MSC 2000: 06F20, 08B99</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">Collections:</th><td valign="top" class="ep_row">UNSPECIFIED</td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">1679</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">Heather Mitchell</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">27 Aug 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">07 Feb 2008 11:59</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=1679;">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=1679">item control page</a></p>
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