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	Semigroup - Wikipedia, the free encyclopedia
		In mathematics, a semigroup is an algebraic structure consisting of a set S closed under an associative binary operation.
		A semigroup whose operation is idempotent is a band.
		A semigroup whose operation is idempotent and commutative is a semilattice.
	en.wikipedia.org /wiki/Semigroup (1346 words)

	Bicyclic semigroup - Wikipedia, the free encyclopedia
		In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups.
		The bicyclic semigroup is the free semigroup on two generators p and q, under the relation p q = 1.
		The bicyclic semigroup has the property that the image of any morphism φ from B to another semigroup S is either cyclic, or it is an isomorphic copy of B.
	en.wikipedia.org /wiki/Bicyclic_semigroup (1006 words)

	Bicyclists - Hutchinson encyclopedia article about Bicyclists
		The bicycle is an energy-efficient, nonpolluting form of transport, and it is estimated that 800 million bicycles are in use throughout the world – outnumbering cars three to one.
		Special bicycles with fat tyres, a strong frame, and more gears than conventional bicycles, designed to be ridden on rough terrain, have become popular since the 1970s; the first purpose-built mountain bikes went on sale in 1979.
		Bicycle use in the UK Although one in three households own a bicycle, average use is only about 6 km/3.7 mi per week per household.
	encyclopedia.farlex.com /Bicyclists (568 words)

	Semigroup - Encyclopedia, History, Geography and Biography
		A semigroup with an identity element is a monoid.
		Two semigroups S and T are said to be isomorphic if there is a bijection f : S ↔ T with the property that, for any elements a, b in S, f(ab) = f(a)f(b).
		If a monogenic semigroup is infinite then it is isomorphic to the semigroup of positive integers with the operation of addition.If it is finite and nonempty, then it must contain at least one idempotent.It follows that every nonempty periodic semigroup has at least one idempotent.
	www.arikah.com /encyclopedia/Semigroup (807 words)

	PlanetMath: regular semigroup
		In an inverse semigroup the set of idempotents is a subsemigroup, in particular a commutative band.
		An example of an inverse semigroup is the bicyclic semigroup.
		In particular, a regular semigroup with one idempotent is a group: as such, many interesting subclasses of regular semigroups arise from putting conditions on the idempotents.
	www.planetmath.org /encyclopedia/InverseSemigroup.html (254 words)

	Semigroup - ExampleProblems.com
		In mathematics, a semigroup is a set with an associative binary operation on it.
		A semigroup with an identity element is called a monoid.
		A semigroup that has a commutative idempotent operation is a semilattice.
	www.exampleproblems.com /wiki/index.php/Semigroup (891 words)

	Green's relations - Wikipedia, the free encyclopedia
		John Mackintosh Howie, a prominent semigroup theorist, described this work as "so all-pervading that, on encountering a new semigroup, almost the first question one asks is 'What are the Green relations like?'" (Howie 2002).
		The opposite case, found for example in the bicyclic semigroup, is where each element is in an H-class of its own.
		Staying within the world of semigroups, Green's relations can be extended to cover relative ideals, which are subsets that are only ideals with respect to a subsemigroup (Wallace 1963).
	en.wikipedia.org /wiki/Green's_relations (1601 words)

	Semigroup info here at en.12-year.info (Site not responding. Last check: 2007-10-21)
		In mathematics, a semigroup is an algebraic structure of a set S closed low-hanging man an associative binary operation.
		A semigroup formally rests of a pair where S is a hang tough a binary mass alarmed the work of the semigroup.
		A transformation semigroup : some finite semigroup S can be represented by transformations of a (state-) hang tough Q of at better S 1 states.
	en.12-year.info /Semigroup (1380 words)

	Semigroup (Site not responding. Last check: 2007-10-21)
		A semigroup with an identity element is usually called a monoid.
		Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining ee = e and es = s = se for all s ∈ S.
		A transformation semigroup : any finite semigroup S can be represented by transformations of a (state-) set Q of at most S+1 states.
	www.xasa.com /wiki/en/wikipedia/s/se/semigroup_1.html (875 words)

	S.Duplij:BibGluskHTML
		Collins, A universal semigroup, Algebra i Logica 9 (1970), 731-740.
		Ecker, On a semigroup of a linear nonsingular automaton, Math.
		Fajtlowies, Equationally comlete semigroups with involutions, Algebra Universalis 1 (1971-72), 355-358.
	www.math.uni-mannheim.de /~duplij/l-glusk.htm (3652 words)

	Semigroup - Wikipedia Mirror (Site not responding. Last check: 2007-10-21)
		A semigroup is, in effect, an associative groupoid.
		This entry assumes that a semigroup may be empty, and need not have an identity.
		A semigroup that has an idempotent operation is a band.
	www.wiki-mirror.be /index.php/Semigroup (875 words)

	Bibliography (Site not responding. Last check: 2007-10-21)
		Adair, A generalization of the bicyclic semigroup, Semigroup Forum 21 (1980), 13-25.
		Makanjuola and A. Umar, On a certain subsemigroup of the bicyclic semigroup, Comm.
		Shevrin, The bicyclic semigroup is determined by its subsemigroup lattice, Simon Stevin 67 (1993), 49-53.
	www.ciul.ul.pt /~vhf/descalco/node1.html (124 words)

	PlanetMath: regular semigroup
		In a regular semigroup, every principal ideal is generated by an idempotent.
		In an inverse semigroup every principal ideal is generated by a unique idempotent.
		Cross-references: subgroup, subclasses, group, bicyclic semigroup, subsemigroup, idempotent, principal ideal, rings, von Neumann regular, semigroup
	planetmath.org /encyclopedia/RegularSemigroup.html (254 words)

	bicycling - Hutchinson encyclopedia article about bicycling (Site not responding. Last check: 2007-10-21)
		Founded in 1903, every July this event attracts the best riders in the world for a gruelling race through France and neighbouring countries.
		Riding a bicycle for sport, pleasure, or transport.
		Among the main events are the Tour de France, first held in 1903; the Tour of Britain (formerly called the Milk Race), first held in 1951; and the World Professional Road Race Championship, first held at the Neuburgring, Germany, in 1927.
	encyclopedia.farlex.com /bicycling (282 words)

	bicyclic definition from the Dictionary of Words Online (Site not responding. Last check: 2007-10-21)
		to the inner and outer circles of the bicyclic polygon..
		Bicyclic and methene resins - toxicity, ecologicial toxicity and regulatory...
		BICYCLIC AND MENTHENE RESINS, Bicyclic and methene resins,...
	www.dictionaryofwords.com /bicyclic_pag11.html (154 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The operation of a semigroup is most often denoted multiplicatively, that is, x\cdot y or simply xy denotes the result of applying the semigroup operation to the ordered pair (x, y).
		A semigroup formally consists of a pair (S,\cdot_S) where S is a set and a binary function \cdot_S: S \times S \rightarrow S called the operation of the semigroup.
		Any semigroup S may be embedded into a monoid (generally denoted as S^1) simply by adjoining an element e not in S and defining es = s = se for all s ∈ S ∪.
	www.maxpedia.org /cgi-bin/mp/m.pl?la=en&sw=semigroup (346 words)

	Home Page of Publication List (Site not responding. Last check: 2007-10-21)
		The Jacobson radical of semigroup rings of commutative semigroups, J. of Algebra, 109 (1) (1987), 266-280.
		Nilpotent semigroups and semigroup algebras (with J. Okninski), J. Algebra, 169 (3) (1994), 984--1011.
		Semigroup algebras that are principal ideal rings (with J. Okninski), J. Algebra, 183 (1996), 837--863.
	homepages.vub.ac.be /~efjesper/public.html (1457 words)

	Abstracts/Résumés
		Bicyclic units have an important role in the theory of units in the integral group ring of a finite group.
		First we give a description of (prime contracted) semigroup algebras K[S] that are hereditary and Noetherian when S is either a Malcev nilpotent monoid, a cancellative monoid or a monoid extension of a finite non-null Rees matrix semigroup.
		The case where S is a semigroup, i.e., a family closed under multiplication, has received a great deal of attention in the last decade or so.
	camel.math.ca /Events/summer99/abstract.htm (12220 words)

	descalco (Site not responding. Last check: 2007-10-21)
		The bicyclic monoid is one of the most fundamental semigroups.
		9, Sec 3.4] references are given to a number of applications of the bicyclic monoid to topics outside semigroup theory.
		The bicyclic monoid is known to have several remarkable properties, one of which is that it is completely determined by its lattice of subsemigroups; see [
	www.ciul.ul.pt /~vhf/descalco/descalco.html (376 words)

	index
		This is the manuscript of a talk given at the Center of Algebra at the University of Lisbon (CAUL) (10/19/01) and at Northern Illinois University (7/26/02).
		This is the manuscript of an invited talk given at the International Conference on Semigroups, Lisbon, July 12-15,2005.
		Tese are the slides of a presentation at the workshop on computational aspects of semigroup theory at the University of St. Andrews, September 5-9, 2006.
	www.math.niu.edu /~don (406 words)

	AMCA: Polyhedral convex cones and the equational theory of the bicyclic semigroup by Francis J. Pastijn (Site not responding. Last check: 2007-10-21)
		AMCA: Polyhedral convex cones and the equational theory of the bicyclic semigroup by Francis J. Pastijn
		Polyhedral convex cones and the equational theory of the bicyclic semigroup
		As a consequence, given any semigroup identity, it is decidable whether or not the variety determined by this identity contains simple semigroups which are not completely simple.
	at.yorku.ca /c/a/i/g/04.htm (207 words)

	1995
		Pierre Antoine Grillet, A precedence theorem for semigroups, 77-81.
		Boris M. Schein, Semigroups of cosets of semigroups: variations on a Dubreil theme, 171-182.
		We use some results of the semigroup theory to obtain an existence theorem for the initial value problem with homogeneous Dirichlet boundary conditions.
	www.imub.ub.es /collect/1995.html (797 words)

	Index CMUC 1960-1994
		Baayen P.C., Hedrl\'{\i }n Z. Commutative polynomial semigroups on a segment4:4 (1963), pp.
		Glastad B., Hopkins G. Commutative semigroup rings which are principal ideal rings21:2 (1980), pp.
		Ku\v{c}era L. On the monoids of homomorphisms of semigroups with unity23:2 (1982), pp.
	www.emis.de /journals/CMUC/cmucinde/cv6094.htm (14821 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		A semigroup presentation defines a semigroup in terms of generators and defining relations between these generators.
		It is very much like a group presentation, except that one is not allowed to use inverses when manipulating words.
		Does there exist an infinite semigroup S such that the finitary power semigroup Pf(S) is finitely presented?
	www-maths.mcs.st-andrews.ac.uk /pg/pure/Algebra/Research/spresns.html (162 words)

	Untitled Document
		Furthermore, we generalized the group ring case to semigroup rings of finite semigroups of which the rational semigroup algebra is semisimple.
		Parmenter [84] discovered that the Bass cyclic units together with another kind of units, namely the f-unitary units, generate a subgroup of finite index in the unit group of the integral group ring of five groups of order 16 (including the two groups mentioned) and this despite the existence of exceptional components.
		Furthermore, we obtained a characterization of semigroup algebras k[S], over infinite fields k and semigroups S generated by periodic elements, for which the unit group satisfies a group identity.
	student.vub.ac.be /~andooms/research.htm (4659 words)

	bicyclic definition from the Dictionary of Words Online (Site not responding. Last check: 2007-10-21)
		bicyclic adj : having molecules consisting of two fused rings
		In practice, this means that the bicyclic semigroup can be found in...
		Bicyclic molecule You can click on this message to see their list of...
	www.dictionaryofwords.com /bicyclic_pag1.html (352 words)

	Springer Online Reference Works
		The most important examples of bi-simple but not completely-simple semi-groups are: the bicyclic semi-groups and the four-spiral semi-group
		It is isomorphic to a Rees semi-group of matrix type over a bicyclic semi-group with generators
		J.M. Howie, "An introduction to semigroup theory", Acad.
	eom.springer.de /s/s085300.htm (640 words)

	[No title]
		Description: An inverse semigroup is a semigroup in which every element has a unique generalised inverse.
		Of course a group is an inverse semigroup, but the converse is not necessarily true.
		The good thing about Clifford semigroups is that their structure can be broken down to groups and partially ordered sets.
	maths.york.ac.uk /moodle/local/project/list.php?courseid=299 (12997 words)

	Mathematics Tasmania Publications Page
		Kelarev A, 'The group units of a commutative semigroup ring', Journal of Algebra 170 902-912 (1994).
		Kelarev AV, 'On the weak permutation property for the bicyclic semigroup', Semigroup Forum 48 253-254 (1994).
		Kelarev A, 'On the description of radicals of semigroup algebras of commutative semigroups.', Izvestiya Vysshikh Uchebnykh Zavedenii Matematika 6 12-18 (1995).
	www.maths.utas.edu.au /HomePage/papers/Publications1996.html (2549 words)

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