
	Where results make sense

Topic: Free monoid

	Free semigroup - Wikipedia, the free encyclopedia
		In abstract algebra, the free monoid on a set A is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from A, with the binary operation of concatenation.
		More generally, a monoid (or semigroup) S is described as free if it is isomorphic to the free monoid (or semigroup) on some set.
		As the name implies, free monoids and semigroups are those objects which satisfy the usual universal property defining free objects, in the respective categories of monoids and semigroups.
	en.wikipedia.org /wiki/Free_semigroup (485 words)

	Monoid - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-22)
		In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single, associative binary operation and an identity element.
		A monoid whose operation is commutative is called a commutative monoid (or, less commonly, an abelian monoid).
		The axioms required of a monoid operation are exactly those required of morphism composition when restricted to the set of all morphisms which start and end at a given object (i.e.
	en.wikipedia.org /wiki/Monoid (1059 words)

	Free semigroup -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		More generally, a monoid (or semigroup) S is described as free if it is (additional info and facts about isomorphic) isomorphic to the free monoid (or semigroup) on some set.
		Each free semigroup (or monoid) S has exactly one set of free generators, the (additional info and facts about cardinality) cardinality of which is called the rank of S.
		As the name implies, free monoids and semigroups are those objects which satisfy the usual (additional info and facts about universal property) universal property defining (additional info and facts about free object) free objects, in the respective (additional info and facts about categories) categories of monoids and semigroups.
	www.absoluteastronomy.com /encyclopedia/f/fr/free_semigroup.htm (480 words)

	Free object -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		The idea of a free object in (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics is one of the basics of (additional info and facts about abstract algebra) abstract algebra.
		These are rather simpler than free groups: the free monoid on a set X, is the monoid of all finite (A linear sequence of symbols (characters or words or phrases)) strings using X as alphabet, with operation (The act of linking together as in a series or chain) concatenation of strings.
		Free objects are created by a (additional info and facts about left adjoint) left adjoint G to F: for a set X the free object on X as 'generators' is G(X).
	www.absoluteastronomy.com /encyclopedia/f/fr/free_object.htm (568 words)

	Monoid: Definition and Links by Encyclopedian.com - All about Monoid
		A monoid is a pair (M,), where M is a set and is a binary operation on M, obeying the following rules:
		In other words, a monoid is a semigroup with an identity element.
		It is possible to view categories as generalizations of monoids: the composition of morphism in a category shares all properties of a monoid operation except that not all pairs of morphisms may be composed.
	www.encyclopedian.com /mo/Monoid.html (655 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Finitely presented semigroups are obtained by factoring a free semigroup by a set of relations (a generating set for the congruence), ie, a set of pairs of words in the free semigroup.
		free monoid) are different from the generators of the finitely presented semigroup (resp.
		free monoid) are not elements of the finitely presented semigroup (resp.
	www-groups.dcs.st-and.ac.uk /~gap/Manuals/doc/build/fpsemi.msk (1280 words)

	Monoid ring: Definition and Links by Encyclopedian.com - All about Monoid ring
		In abstract algebra, a monoid ring refers to a procedure which constructs a new ring from a given ring and a monoid.
		It is a free R-module generated by the elements 1 - g, for g in G.
		Given a ring and the monoid of the non-negative integers, N, we obtain the ring of polynomials over that ring.
	www.encyclopedian.com /mo/Monoid-ring.html (252 words)

	Free object (Site not responding. Last check: 2007-10-22)
		These are rather simpler than freegroups: the free monoid on a set X, is the monoid of all finite strings using X as alphabet, with operation concatenation of strings.
		In general, the setting for a free object is like this: a category C of algebraic structures (sets plusoperations, obeying some laws) has a functor F to Sets, thecategory of sets and functions, that simply ignores the operations.
		Free objectsare created by a left adjoint G to F: for a setX the free object on X as 'generators' is G(X).
	www.therfcc.org /free-object-156304.html (416 words)

	Natural number - Wikipedia, the free encyclopedia
		This turns the natural numbers (N, +) into a commutative monoid with identity element 0, the so-called free monoid with one generator.
		This monoid satisfies the cancellation property and can therefore be embedded in a group.
		This turns (N, ×) into a commutative monoid with identity element 1; a generator set for this monoid is the set of prime numbers.
	en.wikipedia.org /wiki/Natural_number (1612 words)

	6. Relating the Submonoid and Subalgebra Membership Problems in Monoids and Monoid Rings
		Submonoids in free monoids are used in the theory of codes, but codes (as regular languages) are usually studied using techniques from formal language theory.
		Hence the submonoid cannot be described adequately in the monoid ring using the right ideal congruence as in the subgroup case studied before.
		The next theorem states that the submonoid problem for a monoid is equivalent to a special instance of the subalgebra membership problem in the corresponding monoid ring.
	www.mathematik.uni-kl.de /~zca/Reports_on_ca/14/paper_html/node6.html (348 words)

	Free monoid (Site not responding. Last check: 2007-10-22)
		In abstract algebra, the free monoid on a set A is the monoid whose elements are all thefinite sequences of zero or more elements from A, with the binary operation of concatenation.
		Each free semigroup (or monoid) S has exactly one setof free generators, the cardinality of which is called the rank ofS.
		As the name implies, free semigroups and monoids are those objects which satisfy the usual universal property defining free objects, inthe respective categories of semigroups and monoids.
	www.therfcc.org /free-monoid-210453.html (317 words)

	Monoid
		Monoids and Semigroups With Applications: Proceedings of the Berkeley Workshop in Monoids, Berkeley, 31 July - 5 August 1989
		For instance, it is perfectly possible to have a monoid in which exist two elements a and b and such that a*b = a holds even though b isn't the identity element.
		All text is available under the terms of the GNU Free Documentation License.
	www.news-server.org /m/mo/monoid.html (706 words)

	Monoid - Wikipedia
		The set of all finite strings (including the empty string) over some fixed alphabet Σ, with string concatenation as the operation.
		Many definitions and theorems about monoids may also be proved for categories.
		Content is available under GNU Free Documentation License.
	nostalgia.wikipedia.org /wiki/Monoid (576 words)

	LINEAR NUMBERS 0
		Free algebrae and alternative definitions of the Hessenberg operations in the ordinal numbers.
		in the Hessenberg natural operations is isomorphic with the free semiring of α many generators in the category of abelian semirings ;or isomorphic with the algebra of polynomial symbols of α inderminates of the type of algebra of semirings with constants the natural numbers.
		b) by the free algebras of the polynomial symbols of the commutative semirings with unit.
	www.softlab.ece.ntua.gr /~kyritsis/PapersInMaths/InfinityandStochastics/FreeHB.htm (1746 words)

	Introduction (Site not responding. Last check: 2007-10-22)
		A rewrite monoid M is a finitely presented monoid in which equality between elements of M, called words or strings, is decidable via a sequence of rewriting equations, called reduction relations, rules, or equations.
		If a rewrite monoid M is confluent its reduction relations, or more specifically its reduction machine, can be used to reduce words in M to their irreducible normal forms under the given ordering, and so the word problem for M can be efficiently solved.
		The objects are the rewrite monoids and the morphisms are monoid homomorphisms.
	www.dtr.isy.liu.se /Magma/text227.html (317 words)

	The Dimensional Ladder
		Functors Definition Examples: a functor from the free category on an object, a morphism, an isomorphism, an endo, an auto Example: a functor from a group G to Set is a set acted on by G, or G-set.
		A tricategory with one object is a monoidal bicategory.
		Quantum Groups algebras, coalgebras, bialgebras (in a general monoidal category) the category of representations of an algebra the monoidal category of representations of a bialgebra the braided monoidal category of representations of a quasitriangular bialgebra the symmetric monoidal category of representations of a triangular bialgebra the monoidal (resp.
	math.ucr.edu /home/baez/hda/dimensional_ladder.html (2262 words)

	Read about Free object at WorldVillage Encyclopedia. Research Free object and learn about Free object here! (Site not responding. Last check: 2007-10-22)
		generators and relations', we can say that in general a free object of a certain specific algebraic type will have 'generators and no relations'.
		These are rather simpler than free groups: the free monoid on a set X, is the monoid of all finite strings using X as alphabet, with operation
		In general, the setting for a free object is like this: a category C of
	encyclopedia.worldvillage.com /s/b/Free_object (387 words)

	AlgebraicStructures - PineWiki
		Let A be the free monoid over { a, b, c }, and let B be the subalgebra generated by aaa.
		In a free semigroup, x(yz) = (xy)z, always, because of the associativity axiom, but xy is never equal to x for any x and y, xy is never equal to yx, etc. In a free monoid, xe = ex = x, but xy is never equal to x unless y = e, and so forth.
		Fortunately this reversal operation is an isomorphism between the two monoids, and in general we can show that any free algebra for a given class with a given base set is unique up to isomorphism, which means that while there may be more than one such algebra, there is only one isomorphism equivalence class.
	pine.cs.yale.edu /pinewiki/AlgebraicStructures (5539 words)

	Lambek calculus papers by Mati Pentus (Site not responding. Last check: 2007-10-22)
		In this paper the Chomsky Conjecture is proved: all languages recognized by the Lambek calculus are context free.
		We prove that the Lambek syntactic calculus allowing empty premises is complete with respect to the class of all free monoid models (i.
		We prove that the conjoinability relation (on syntactic types) is decidable and that it is complete with respect to the free group interpretation.
	lpcs.math.msu.su /~pentus/abstr.htm (564 words)

	Words
		Given a plactic monoid P, and a word w from the ordered monoid that its based on, return the element of P corresponding to the Knuth equivalence class of w.
		Given a plactic monoid P, and a sequence of elements from the ordered monoid that its based on, return the element of P corresponding to the Knuth equivalence class of w_1...
		Given a plactic monoid P and a tableau t which are both associated with the same ordered monoid, return the element of P which is uniquely associated to t.
	www.math.lsu.edu /magma/text1359.htm (1295 words)

	Fields Institute - Workshop on Profinite Groups and Applications
		Thus, a natural question about the structure of (finitely generated) free profinite semigroups is which profinite groups can appear as its maximal subgroups.
		The technique which we have developed consists in producing maximal subgroups by studying the dynamics of the monoid of continuous endomorphisms of finitely generated free profinite semigroups, which is a profinite monoid under the pointwise convergence topology.
		A group G is called conjugacy separable if any two non-conjugate elements map to non-conjugate elements in some finite quotient of G; and G is called subgroup separable if failure of an element to lie in a given finitely generated subgroup can again be detected by passage to some finite quotient.
	www.fields.utoronto.ca /programs/scientific/05-06/profinite/abstracts.html (1082 words)

	Monoids (Site not responding. Last check: 2007-10-22)
		A monoid is an algebraic structure that captures many
		A monoid is an algebraic structure that captures most collection and aggregate types.
		Formally, a monoid is a pair of an associative function, called the merge function, and a value, which is the left and right identity of the merge function.
	ranger.uta.edu /~fegaras/talk98/tsld012.htm (87 words)

	Free semigroup (Site not responding. Last check: 2007-10-22)
		In abstract algebra, the free monoid on a set A is the monoid whose elements are all the finite sequences of zero or more elements from A, with the binary operation of concatenation.
		The unique sequence of zero letters (empty string) often denoted ε, is the identity element.
		The free semigroup on A is the subsemigroup of A
	www.sciencedaily.com /encyclopedia/free_semigroup (387 words)

	Relations and Presentations
		The group defined by this presentation is the free group mod the normal subgroup implied by the relators.
		A monoid is almost a group, but it doesn't have to have inverses.
		Consider the free monoid on A and B, with the relation A = B. There is no relator A/B, because there is no B inverse.
	www.mathreference.com /grp-free,relat.html (794 words)

	[No title]
		The free (commutative) monoid on one element x has a submonoid consisting of 1,x^3,x^5,x^6 and all x^n for n > 7 is not free.
		John Stell asked when to expect subobjects of free objects to be free and observed that such is the case for modules over prinicpal ideal domains.
		He points out that subalgebras of free algebras are free if the theory consists of just one binary operation and no equations.
	www.mta.ca /%7Ecat-dist/catlist/1999/substructures (888 words)

Try your search on: Qwika (all wikis)