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Topic: 2-monoid

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Monoid - Wikipedia, the free encyclopedia In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single, associative binary operation and an identity element. 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. A monoid whose operation is commutative is called a commutative monoid (or, less commonly, an abelian monoid). en.wikipedia.org /wiki/Monoid

Monoid ring - Wikipedia, the free encyclopedia In abstract algebra, a monoid ring is a procedure which constructs a new ring from a given ring and a monoid. The set of all these functions, together with these two operations, forms a ring, the monoid ring of R over G; it is denoted by R[G]. Let R be a ring and G be a monoid. en.wikipedia.org /wiki/Monoid_ring

PlanetMath: monoid This is version 2 of monoid, born on 2001-10-19, modified 2004-02-02. Object id is 389, canonical name is Monoid. planetmath.org /encyclopedia/Monoid.html

GAP Manual: 87 Monoids and Semigroups Then the functions which construct monoids and semigroups and the functions which test whether a given object is a monoid or a semigroup are described (see SemiGroup, IsSemiGroup, Monoid and IsMonoid). Monoids and semigroups are domains, so every set theoretic function for domains is applicable to them (see Set Functions for Monoids). Standard monoid elements may be compared with objects of other types while generic monoid elements may disallow such a comparison. schmidt.nuigalway.ie /gap/CHAP087.htm

Based on Abstract Algebra Monoid comprehensions are based on the notion of monoid homomorphisms from abstract algebra. It maps the zero element of the input monoid to the zero of the output monoid, it replaces the unit function with function f, and it distributes over merge. For example, the homomorphism from the set monoid to the + monoid applies f to every element of the set and adds together the results. ranger.uta.edu /~fegaras/talk98/tsld017.htm

MonoidOperation Monoid operations are required to be associative, but they are not required to be commutative. A Monoid Operation is a special sort of Binary Function. The type of the Monoid Operation's first argument and second argument, and also the type returned when the Monoid Operation is returned. www.sgi.com /tech/stl/MonoidOperation.html

monoid1 Its first argument should be a monoid M and the second and third arguments should be elements of M. When applied to M, a, and b, it denotes the fact that a is a divisor of b in M. This means that there are u,v in carrier(M) such that uav=b. This example represents the monoid which has as elements all positive and negative even numbers, the monoid operation is binary addition, inverses are the negative of the element and the identity is the zero element. Its argument should be a monoid M. When applied to M, it denotes the submonoid of M consisting of all invertible elements in M. This is a group. www.openmath.org /cocoon/openmath/cdfiles2/cd/monoid1.html

Introduction The objects are the rewrite monoids and the morphisms are monoid homomorphisms. 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. www.math.niu.edu /help/math/magmahelp/text224.html

Character Formulas for q-Rook Monoid Algebras (ResearchIndex) 3 rook monoid (context) - Halverson, the - 2001 1.0: A Specht Module Analog for the Rook Monoid - Cheryl Grood Department (2001) 4 Representations of the rook monoid (context) - Solomon citeseer.ist.psu.edu /485816.html

MATHS: Monoids A monoid is an abstract model of most situations in which a set of actions tend to change objects. Monoid have much of the structure normally taught as part of group theory. What is the smallest monoid with unit 1, operation and element x, such that x x x=1? www.csci.csusb.edu /dick/maths/math_33_Monoids.html

Conscientia Peccati, Monoid, Stillstand Monoid is a term from the area of mathematics: A monoid is a closed half group with a neutral element. The live sound of Monoid is much harder and more organic than on the tape and CDR releases. Most people will have no idea what a monoid is, but it sounds familiar in a certain way. www.ipsi.fraunhofer.de /~steineba/m01.htm

GAP Share Package "Monoid". MONOID provides functions that determine the size of a transformation monoid M, can list the elements of M or decide membership of any transformation of degree n in M. Moreover, the Green class structure of M can be determined. MONOID is a package of GAP functions for transformation monoids and related objects. Relations of degree n can be used to generate a monoid. www.gap-system.org /oldsite/Share/monoid.html

Monoids 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. A monoid is an algebraic structure that captures most collection and aggregate types. A monoid is an algebraic structure that captures many ranger.uta.edu /~fegaras/talk98/tsld012.htm

Tableaux Given a tableau monoid M, a sequence of positive integers S which is a partition, and a sequence of non--negative integers C, then return the set of all tableau from M having shape S and content C (see section Properties for definition of content). Given a tableau monoid M, and a sequence of positive integers S which is a partition, return a random standard tableau from M of shape S. If a tableau monoid M is not specified then the monoid over the positive integers is used. Given the tableau monoid M over the positive integers, and a sequence of sequences of non-negative integers Q, return the tableau with the elements of Q as its rows. www.umich.edu /~gpcc/scs/magma/text1174.htm

fpsemi.msk Sci., University of St. Andrews, Scotland %Y Copyright (C) 2002 The GAP Group %% \Chapter{Finitely Presented Semigroups and Monoids} A *finitely presented semigroup* (resp. *finitely presented monoid*) is a quotient of a free 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

GAP Manual: 80 Garside and braid monoids and groups Garside monoids are a general class of monoids whose most famous examples are the braid and dual braid monoids. A Garside monoid embeds into its group of fractions, which is called a Garside group (it may be that a Garside group has several distinct Garside structures, as we will see is the case for Braid groups of finite Coxeter groups). is in the group but not the monoid, it is represented in fraction normal form where as a special convention the inverses of the atoms are represented by negating the corresponding integer. www.math.jussieu.fr /~jmichel/htm/CHAP080.htm

Words This plactic monoid is in fact isomorphic to the monoid of tableaux over the same generators. The most important example is the monoid of words generated by the positive integers, though Magma also allows the creation of finitely generated ordered monoids. Given the plactic monoid P over the positive integers, and a sequence of integers, return the element of P corresponding to the Knuth equivalence class of i_1... www.math.lsu.edu /magma/text1359.htm

Math Forum: Magic Squares: 'Multiplication' in a new context If (M,*,1) is a commutative monoid and if M has a subset P such that M is freely generated by P as a commutative monoid, we say that M is a free commutative monoid. Let (M,*,1) be a monoid and let P be a subset of M. We say that M is freely generated by P if the unique factorization theorem holds with respect to P, i.e. Thus, a commutative monoid is a monoid (M,*,1) in which the operation * is commutative. www.mathforum.com /alejandre/magic.square/adler/product.html

Informatica Monoid action level is defined as monoid element (word) action on module element as an operator. Two algebraic structures are employed: Gaussian monoid and a certain module being compatible with a monoid. For both monoid and module, presentation and action level attributes are defined. www.vtex.lt /informatica/htm/INFO552.htm

SEMIGROUPE and MONOID MONOID provides functions that determine the size of a transformation monoid M, can list the elements of M or decide membership of any transformation of degree n in M. MONOID was developed by Steve Linton, Goetz Pfeiffer, Nik Ruskuc, Edmund Robertson. It is a package of GAP functions for transformation monoids and related objects. www.inria.fr /actualites/colloques/1998/ALAPEDESMONOID-eng.html

11. Theory Ensembles Notice that the theory of a monoid as presented here is suitable for concept formulation and proof in a single monoid. Much of mathematics deals with the study of structures such as monoids, fields, metric spaces, or vector spaces, which consist of an underlying set S, some distinguished constants in S, and one or more functions on S. However, there is no way to talk about monoid homomorphisms between different monoids. imps.mcmaster.ca /manual/node16.html

OrderedMonoid The reason for making a separate class for ordered monoids is that monoid rings can be implemented more efficiently for them - an element of the monoid ring can be stored as a sorted list, each element of which is a pair consisting of an element of the monoid and a coefficient. An ordered monoid is a multiplicative monoid together with an ordering of its elements. A free commutative ordered monoid can be created with monoid. www.math.umn.edu /systems_guide/Macaulay2/html/0315.html

Citebase - The quantic monoid and degenerate quantized enveloping algebras 25 [Re3] M. Reineke:The monoid of families of quiver representations. Its monoid ring is shown to be isomorphic to a degenerate quantized enveloping algebra. All these results are proved by a realization in terms of representations of quivers, namely as the monoid of generic extensions of a quiver with automorphism. citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0206095

Syntactic Semigroup The syntactic monoid Syn(L) of L is the monoid is a free monoid with a generating set A and catenation of words as operation. So, the factor language of every sofic system has a finite syntactic monoid. www.math.usf.edu /~jonoska/symbolic/node14.html

Conscientia Peccati, Monoid, Stillstand There will be another Monoid CD this year by DTA records, and I really hope to publish some of the Conscientia Peccati stuff I have waiting since back in 1999 this year Compilation appearances on Crunch Pod Media, Section 19 and other labels are in progress. Finished a full demo for the new Monoid CD and am now looking for some label. There is a new Monoid CD release named “Pain Addiction” planned for September. www.ipsi.fraunhofer.de /~steineba/news.htm

Monoid of Multisets and Subsets The monoid of multisets over a set is constructed as such monoid where the target group is the group of natural numbers with addition. The monoid of functions yielding elements of a group is introduced. Moreover, the generalization of group operation onto the operation on subsets is present. www.mizar.org /JFM/Vol4/monoid_1.html

Data.Monoid Declaration of the Monoid class, and instances for list and functions. , and these should satisfy the monoid laws. www.complete.org /fs/hclr/base/Data.Monoid.html

All Countable Monoids Embed In The Monoid Of The Infinite Random Graph (ResearchIndex) We also prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of the monoid of R. (Update) As a corollary, the monoid of R does not satisfy any non-trivial semigroup identity. Abstract: We prove that the endomorphism monoid of the infinite random graph R contains as a submonoid an isomorphic copy of each countable monoid. citeseer.ist.psu.edu /580877.html

Monoid of graphical patterns in Let us remember that a monoid is defined by a semigroup with identity element over its operation. Graphical patterns that arise from evolutions of rule 110, obey other rules that we can study in this paper, but in general, patterns like triangles can be used for covering the discrete 2-space. The covers themself define an additive discrete monoid. computacion.cs.cinvestav.mx /~acaceres/docs/h110/node2.html

DC MetaData for: The isomorphism problem for commutative monoid rings This means that the underlying monoid is shown to be determined (up to isomorphism) by the corresponding monoid ring. Abstract: By substantial changes and corrections in Demushkin's old paper the essentially final positive answer to the isomorphism problem for monoid rings of submonoids of Z Thereafter the positive answer to the analogous question for the `dual' objects -descrete Hodge algebras - is derived. www.mathematik.uni-osnabrueck.de /preprints/shadow/calg9611a.html

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