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Topic: Free semigroup

  Semigroup - Wikipedia, the free encyclopedia
A semigroup with an identity element is a monoid.
A semigroup whose operation is idempotent is a band.
A semigroup whose operation is idempotent and commutes is a semilattice.
en.wikipedia.org /wiki/Semigroup   (861 words)

 Free object - Wikipedia, the free encyclopedia
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 concatenation of strings.
As that example suggests, free objects look like constructions from syntax; and we can reverse that to some extent by saying that major uses of syntax can be explained and characterised as free objects, in a way that makes apparently heavy 'punctuation' explicable (and more memorable).
Free objects are created by a left adjoint G to F: for a set X the free object on X as 'generators' is G(X).
en.wikipedia.org /wiki/Free_object   (450 words)

 [ref] 48 Finitely Presented Semigroups
Finitely presented semigroups are obtained by factoring a free semigroup by a set of relations (a generating set for the congrucence), ie, a set of pairs of words in the free semigroup.
Also note that the generators of the free semigroup are different from the generators of the finitely presented semigroup (even though they are displayed by the same names).
This means that words in the generators of the free semigroup are not elements of the finitely presented semigroup.
sylow.slu.edu /gap/htm/ref/CHAP048.htm   (1332 words)

 MATHS: Semigroups
A semigroup that has a commutative operation (so that a combined with b is the same as b combined with a) is said to be Abelian.
A common example of a semigroup is the free semigroup generated by a set of atomic elements A by concatenating them.
If f is a morphism from the semigroup S1 to S2 then it is a map and so define a partition of S1.Set into a collection of sets which themselves form a semigroup with an operation defined by the inverses image of the operation in the second semigroup S2.op.
www.csci.csusb.edu /dick/maths/math_32_Semigroups.html   (1921 words)

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)

 Free semigroup: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-10-08)
In mathematics, a semigroup is a set with an associative binary operation on it....
Each free semigroup (or monoid) S has exactly one set of free generators, EHandler: no quick summary.
(free monoids and semigroups are those objects which satisfy the usual universal property universal property quick summary:
www.absoluteastronomy.com /encyclopedia/f/fr/free_semigroup.htm   (1294 words)

 Wikinfo | Semigroup   (Site not responding. Last check: 2007-10-08)
In mathematics, a semigroup is a set with an associative binary operation on it.
A semigroup with an identity element is called 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).
www.wikinfo.org /wiki.php?title=Semigroup   (746 words)

 FPM 1999, vol. 5, no. 1, pp. 283-305   (Site not responding. Last check: 2007-10-08)
The third one is the free semigroup of continuum rank consisting of all non-trivial periodic group varieties.
The fifth one is a semigroup without idempotents containing a subsemigroup isomorphic to a free semigroup of continuum rank.
In conclusion, the indices of nilpotence of semigroups
www.univie.ac.at /EMIS/journals/FPM/eng/99/991/99116t.htm   (195 words)

 [ref] 49 Semigroups
Note that for a transformation semigroup to be a transformation monoid we necessarily require the identity transformation to be an element.
An equivalence or a congruence on a semigroup is the equivalence or congruence on the semigroup considered as a magma.
Recall that a Rees Matrix semigroup is constructed from a semigroup (the underlying semigroup), and a matrix.
www-groups.dcs.st-and.ac.uk /~gap/Manuals/doc/htm/ref/CHAP049.htm   (1238 words)

 [No title]
For an extension of this matter to the Gaussian numbers, I regarded the two semigroups as hyperbolic motions in the hypberbolic 2-space H_2, and their role for a decomposition of the modular group PSL(2,Z).
The semigroup H for PSL(2,Z[i]) is generated by 7 elements and is not a free semigroup - the situation increases in complexity.
The 7 generators of the semigroup H are: a: (1,1,0,1) b: (1,0,1,1) c: (1,i,0,1) d: (1,0,-i,1) e:...
www.math.niu.edu /~rusin/known-math/94/contfra_cpx   (862 words)

 [No title]   (Site not responding. Last check: 2007-10-08)
semigroup3 http://www.openmath.org/cd/semigroup3.ocd 2006-06-01 2004-06-01 3 1 experimental Semigroup constructions Initiated by Arjeh M. Cohen 2003-10-02 cyclic_semigroup This symbol denotes the cyclic semigroup with a cycle of length l and a tail of length k.
When applied to X, it refers to the semigroup of all functions from X to X if X is a set and to {1,...,X} if X is an integer, whose binary operation is composition of maps and whose identity element is the identity map on the set X, respectively {1,...,X}.
When evaluated on such an argument, the function represents the free semigroup generated by the entries of the list or set.
www.win.tue.nl /~amc/oz/om/cds/semigroup3.html   (209 words)

 Free semigroup at opensource encyclopedia   (Site not responding. Last check: 2007-10-08)
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 free semigroup on A is the subsemigroup of A
More generally, a semigroup (or monoid) S is described as free if it is isomorphic to the free semigroup (or monoid) on some set.
www.wiki.tatet.com /Free_monoid.html   (345 words)

 [No title]
The input of the semigroup programs is a Cayley graph of the semigroup (the table of type: elements on generators) presented as text file.
The maximal size of semigroups we consider on standard personal computer was some thousands elements with the number of generators about a half.
The set of locally threshold testable semigroups forms a quasivariety of semigroups and we present a basis of quasiidentities of the quasivariety.
www.cs.biu.ac.il /~trakht/kyotorims.rep   (1114 words)

 The Construction of Free Semigroups and their Elements   (Site not responding. Last check: 2007-10-08)
Construct the free semigroup F on n generators, where n is a positive integer.
Construct the free monoid F on n generators, where n is a positive integer.
Given a semigroup S defined on r generators and a sequence Q = [i_1,..., i_s] of integers lying in the range [1, r], construct the word G.(i_1) * G.(i_2) *...
www.math.uiuc.edu /Software/magma/text179.html   (331 words)

 Research interests (Bella Rozenblat)   (Site not responding. Last check: 2007-10-08)
Questions of decidability of first-order theories for semigroups and other algebraic structures; equations in semigroups and groups; genetics.
The criterion for decidability of an elementary theory of an arbitrary completely simple semigroup was established in [14].
The membership problem for recursively enumerable subsets of N was interpreted in elementary theories of corresponding Rees matrix semigroups over the 3-element group [13].
www.cs.bgu.ac.il /~bella/research.html   (210 words)

Abstract: Let S be a finitely presented semigroup having a minimal left ideal L and a minimal right ideal R. The main result gives a presentation for the group R intersection L. It is obtained by rewriting the relations of S, using the actions of S on its minimal left and minimal right ideals.
The first gives a presentation for a two-sided ideal of a semigroup, and implies that a two-sided ideal of finite index in a finitely presented semigroup is itself finitely presented.
We also prove that in a free semigroup of finite rank a subsemigroup of finite index is finitely presented, and that any ideal which is finitely generated as a subsemigroup is finitely presented.
www-history.mcs.st-and.ac.uk /~edmund/abstracts.html   (1673 words)

 AlgebraicStructures - PineWiki
Let A be the free monoid over { a, b, c }, and let B be the subalgebra generated by aaa.
We've seen examples of various kinds of algebras that have been called "free", such as free magmas, free semigroups, etc. There is in fact a single definition of a free algebra (from a particular class of algebras) that produces each of these specific free algebras.
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.
pine.cs.yale.edu /pinewiki/AlgebraicStructures   (5576 words)

 [ref] 34 Associative Words
Associative words can be multiplied; in free monoids also the computation of an identity is permitted, in free groups also the computation of inverses (see Operations for Associative Words).
Using homomorphisms it is possible to express elements of a group as words in terms of generators, see Expressing group elements as words in generators.
The product of two given associative words is defined as the freely reduced concatenation of the words; so adjacent pairs of a generator and its inverse never occur in words.
www.math.niu.edu /help/math/gap4/ref/CHAP034.htm   (1698 words)

 [ref] 59 Magma Rings
free algebras and free associative algebras, with or without one, where the magma is a free magma or a free semigroup, or a free magma-with-one or a free monoid, respectively.
Note that a free Lie algebra is not a magma ring, because of the additional relations given by the Jacobi identity; see Magma Rings modulo Relations for a generalization of magma rings that covers such structures.
For example, polynomials are elements of a free magma ring, and they have an external representation relying on the special form of the underlying monomials.
faculty.biu.ac.il /~htmldoc/gap4r1/ref/CHAP059.htm   (1073 words)

 [ref] 40 Associative Words   (Site not responding. Last check: 2007-10-08)
These words can be concatenated and may (in free monoids, respectively free groups) permit computation of an identity and of inverses.
Using homomorphisms it is possible to express elements of a group as words in generators, see Expressing group elements as words in generators.
Each free object defines a unique alphabet (and thus a unique family of words) and its generators are simply the words of length one in this alphabet.
www.math.psu.edu /local_doc/gap4/htm/ref/CHAP040.htm   (973 words)

 Pacific Journal of Mathematics - Abstract for 186-1-7 - Gelu Popescu   (Site not responding. Last check: 2007-10-08)
Minimal joint isometric dilations for families of contractive sequences of operators on a Hilbert space are obtained and used to extend the von Neumann inequality and the commutant lifting theorem to our noncommutative setting.
An extension of the Naimark dilation theorem to free semigroups is considered.
This is used to construct a large class of positive definite operator-valued kernels on the unital free semigroup on n generators and to study the class C
nyjm.albany.edu:8000 /PacJ/1998/186-1-7.html   (213 words)

 [ref] 35 Associative Words
is a group, whose generators are represented by symbols (for example a free group, a finitely presented group or a pc group) this function assigns these generators to global variables with the same names.
Unless the syllable representation is specified explicitly when creating the free group/monoid or semigroup, a letter representation is used by default.
For example when creating pc groups (see Pc groups), it is advantageous to use a syllable representation while calculations in free groups usually benefit from using a letter representation.
www.math.sunysb.edu /~sorin/online-docs/gap4r3/htm/ref/CHAP035.htm   (3155 words)

 NewAbelianSquare-FreeDT0L-LanguagesOver4Letters.nb   (Site not responding. Last check: 2007-10-08)
The tool which Thue invented for constructing square-free words, namely the concept of a repetition-free morphism, is still today a basic device in the study of avoidable patterns in words.
Repetition-free morphisms are mappings between free monoids that preserve the repetition-freeness of words.
in [16], where it was shown that a finitely generated semigroup is uniformly repetitive if and only if it is finite.
south.rotol.ramk.fi /keranen/ias2002/NewAbelianSquare-FreeDT0L-LanguagesOver4Letters.html   (3469 words)

Equations in a free inverse semigroup, in: Algebraic systems and their varieties, Math.Zap.Ural.Univ.(Proceedings of the Ural University), Sverdlovsk, pp.117-120 [in Russian] (1982).
Elementary theories of relatively free semigroups with a permutation identity, in: Studying of algebraic systems by means of properties of their subsystems, Math.Zap.Ural.Univ. (Proceedings of the Ural University), Sverdlovsk, pp.
[15] B.V.Rozenblat, On equations in inverse semigroups, in:
www.cs.bgu.ac.il /~bella/cite0.html   (299 words)

 [ref] 46 Semigroups
S is a semigroup with zero true if and only if the semigroup has no proper ideals except for 0.
So, to deal with equivalences and congruences on semigroups, magma funtions are used.
Given a regular D class of a finite semigroup, it can be viewed as a rees matrix semigroup by identifying products which do not lie in the D class with zero.
faculty.biu.ac.il /~htmldoc/gap4r1/ref/CHAP046.htm   (1146 words)

 Maximal Groups in Free Burnside Semigroups   (Site not responding. Last check: 2007-10-08)
The problem of determining whether a free Burnside group finitely generated is finite or not is extremely complex and was raised by Burnside in 1902.
While these semigroups are infinite, Brzozowski conjectured that some properties of finiteness should remain true for the free Burnside semigroups.
-class of the free Burnside semigroup and we prove that it is a circuit.
www.ime.usp.br /~alair/x2e.html   (5833 words)

 Affine actions of a free semigroup on the real line - abstract   (Site not responding. Last check: 2007-10-08)
Affine actions of a free semigroup on the real line
We consider actions of the free semigroup with two generators on the real line, where the generators act as affine maps, one contracting and one expanding, with distinct fixed points.
Then every orbit is dense in a half-line, which leads to the question whether it is, in some sense, uniformly distributed.
www.math.iupui.edu /~mmisiure/bms.html   (87 words)

 AMCA: Absolutely continuous functionals and a Kaplansky theorem for free semigroup algebras by Ken Davidson   (Site not responding. Last check: 2007-10-08)
These functionals are used to help identify the type L part of the free semigroup algebra associated to this representation.
This is the crucial device for establishing a density theorem that the unit ball of \sigma(\mathfrakA
The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
at.yorku.ca /c/a/n/e/49.htm   (133 words)

 Binary operation - All About All   (Site not responding. Last check: 2007-10-08)
That f takes values in the same set S that provides its arguments is the property of closure.
Binary operations are the keystone of algebraic structures studied in abstract algebra: they form part of groups, monoids, semigroups, rings, and more.
Most generally, a magma is a set together with any binary operation defined on it.
www.answers-zone.com /article/Binary_operation   (417 words)

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