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Topic: Monoid algebra

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	String Rewriting and Gröbner Bases - A General Approach to Monoid and Group Rings
		The concept of algebraic simplification is of great importance for the field of symbolic computation in computer algebra.
		The techniques for presenting monoids or groups by string rewriting systems are used to define several types of reduction in monoid and group rings.
		The concepts of saturation and completion are introduced for monoid rings having a finite convergent presentation by a semi-Thue system.
	www.mathematik.uni-kl.de /~zca/Reports_on_ca/16/paper_html/paper.html (189 words)

	[No title]
		Much of the elegance of Joy is due to the simple algebraic structure of its syntax and the simple algebraic structure of its semantics and to the fact that the two structures are so similar.
		Monoids and homomorphisms are familiar from abstract algebra.
		One example is the logarithm function which is a homomorphism from the multiplicative monoid onto the additive monoid.
	www.latrobe.edu.au /philosophy/phimvt/joy/j02maf.html (5835 words)

	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.
		A monoid whose operation is commutative is called a commutative monoid (or, less commonly, an abelian monoid).
		Indeed, the axioms required of a monoid operation are exactly those required of morphism composition when restricted to the set of all morphisms whose source and target is a given object.
	en.wikipedia.org /wiki/Monoid (1364 words)

	Monoid
		A monoid (M,) has the cancellation property (or is cancellative) if for all a, b and c in M, a''
		The axioms required of a monoid operation are exactly those required of a category operation when restricted to the set of all morphisms which start and end at a given object.
		Hence, a monoid is essentially the same thing as a category with a single object.
	www.nebulasearch.com /encyclopedia/article/Monoid.html (694 words)

	Vector Enumeration
		The algebra may be the group algebra of an fp-group, in which case the resulting module will be a matrix representation of the group, or it might be a more general fp-algebra, such as a Hecke algebra or a quotient of a polynomial ring.
		The permutation module of degree 4 of this algebra is presented by one generator (as it is transitive) and the submodule generator b - 1.
		This is represented as a table, with columns indexed by the generators of the algebra, and rows indexed by the basis of the space.
	www.math.lsu.edu /magma/text890.htm (3215 words)

	Monoids and Groups. Group Theory and Symmetries - Numericana
		Monoids are endowed with an associative operation and a neutral element.
		On the other hand, a monoid operator may or may not be commutative (there may or may not be pairs of elements for which xy and yx are different).
		He carved them into the stone of the bridge (although no trace of the original carving is seen, a plaque is now on the bridge to celebrate this famous act of mathematical vandalism).
	home.att.net /~numericana/answer/groups.htm (4881 words)

	[No title]
		Algebras and modules in monoidal model categories Stefan Schwede and Brooke E. Shipley1 Abstract: We construct model category structures for monoids and modules in symmetric monoidal model categories, with appli- cations to symmetric spectra and -spaces.
		N be a cofibration of monoids with M cofibrant in C. Every cofibration of monoids is a* * retract of a regular I-cofibration with I as in Lemma 5.2.
		P is a map of monoids and (iii)P has the universal property of the pushout in the category of monoids.
	www.math.purdue.edu /research/atopology/Schwede-Shipley/last.txt (8006 words)

	AlgebraicStructures - PineWiki
		Most operations on an algebra are defined in terms of operations on the carrier (the set of elements of the algebra).
		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.
		Let C be a class of algebras, where the names and arities of the operations are the same for all algebras in the class, and let S be a set.
	pine.cs.yale.edu /pinewiki/AlgebraicStructures (5576 words)

	Commutative Algebra Seminar, University of Nebraska-Lincoln
		On seminormal monoid rings Abstract: Given a seminormal affine monoid M we consider several monoid properties of M and their connections to ring properties of the associated affine monoid ring K[M] over a field K.
		It is derived from a more general theorem on Gorenstein affine normal monoids M: one can factor K[M] (K a field) by a ``long'' regular sequence in such a way that the quotient is still a normal affine monoid algebra.
		In the case of a polytopal Gorenstein normal monoid E(P), this technique reduces all questions about the Ehrhart h-vector to a normal Gorenstein polytope Q with exactly one interior lattice point.
	www.math.unl.edu /~siyengar2/Seminars/Fall05.html (1307 words)

	Concurrency Abstracts (Site not responding. Last check: )
		Its algebraic structure is essentially that of linear logic, with its morphisms being consequence-preserving renamings of propositions, and with its operations forming the core of a natural concurrent programming language.
		It corresponds to a monoid whose three elements represent strict precedence, lax precedence (simultaneity is permitted), and absence of constraint.
		The algebra is that of a parallel programming language expanded to the language of full linear logic, Girard's axiomatization of which is satisfied by the event space interpretation of this language.
	boole.stanford.edu /abstracts.html (9716 words)

	AMCA: Z-commutativity of Order 4 of the Dihedral Groups by Aleksandar Blazevski (Site not responding. Last check: )
		The Z-commutativity is a generalization of the ordinary commutativity of a monoid M. This concept is formulated in the monoid algebra Z[M].
		A monoid M is called Z-commutative of order n if all the permutational determinants for all the n-tuples from M are zero in Z[M].
		Each finite monoid M with m elements is Z-commutative of order at least m+1.
	at.yorku.ca /c/a/m/b/13.htm (270 words)

	Bibliography
		String rewriting and Gröbner bases - a general approach to monoid and group rings.
		Relating rewriting techniques on monoids and rings: Congruences on monoids and ideals in monoid rings.
		Algorithmic problems in groups, semigroups and inverse monoids.
	www.mathematik.uni-kl.de /~zca/Reports_on_ca/19/paper_html/node8.html (299 words)

	Monoid Algebra
		Here are the algebraic operators and their meaning in terms of the monoid calculus.
		Since we are translating the calculus into the algebra, this means that calculus and algebra are equivalent.
		In fact if we do not do any query unnesting, the 5 first operators are sufficient for the translation.
	lambda.uta.edu /talk98/sld029.htm (66 words)

	Journal of Formalized Mathematics, Index of MML Identifiers
		On the Monoid of Endomorphisms of Universal Algebra and Many Sorted Algebra.
		Algebra of Normal Forms Is a Heyting Algebra.
		Algebraic Group on Fixed-length Bit Integer and its Adaptation to IDEA Cryptography.
	www.mizar.org /JFM/mmlident.html (2155 words)

	Bibliography
		An Extension of Buchberger's Algorithm and Calculations in Enveloping Fields of Lie Algebras.
		Synergy in the theories of Gröbner bases and path algebras.
		Congruemces in Monoids and Ideals in Monoid Rings.
	www.mathematik.uni-kl.de /~zca/Reports_on_ca/16/paper_html/node6.html (571 words)

	MATHS: Algebras
		An algebra is a set of objects (called Set here) plus other documentation (named DOC here) defining constants, operations and axioms.
		The Integers for example with the operations of addition and subtraction with unit 0 is said to be a group (Integer, +, 0, -).
		This network of propositions (ALGEBRA), formalizes the relationship between the documentation of an algebra, the name of the set of ntples, and the type of the objects that fit the algebra.
	www.csci.csusb.edu /dick/maths/math_43_Algebras.html (361 words)

	OUP: UK General Catalogue (Site not responding. Last check: )
		The notions of an algebra and a coalgebra over an operad are introduced, and their properties are investigated.
		The algebraic structure of the singular chain complex of a topological space is explained, and it is shown how the problem of homotopy classification of topological spaces can be solved using this structure.
		Operad methods are applied to computing the homology of iterated loop spaces, investigating the algebraic structure of generalized cohomology theories, describing cohomology of groups and algebras, computing differential in the Adams spectral sequence for the homotopy groups of the spheres, and some other problems.
	www.oup.com /uk/catalogue/?ci=9780821821701 (335 words)

	[No title]
		Let $\G$ be finite directed graph (which, in the representation theory of algebras is called a {\it quiver}).
		The path algebra, denoted $K\G$, is the $K$-algebra with $K$-basis the finite directed paths in $\G$.
		Koszul algebras have appeared in topology, algebraic geometry and in the theory of quantum groups.
	www.mscs.mu.edu /~mikes/CompAlg/green (862 words)

	[No title]
		Has anyone proved that if you take an "algebra" (actually monoid) object in a monoidal biclosed category that has equalizers and coequalizers, then the category of two-sided modules for that algebra is again a monoidal biclosed category.
		Mac Lane did this in 1965 when everything is symmetric (the tensor, the algebra and the modules) under the (surely irrelevant) assumption that the original category is also abelian.
		In response to Michael Barr's question: Theorem: If V is a closed braided monoidal category which is complete and cocomplete then the bicategory V-Mod of V-categories, V-modules (sometimes called V-bimodules, V-distributors or V-profunctors), and V-module morphisms is a monoidal bicategory (meaning the hom of a tricategory with one object).
	www.mta.ca /~cat-dist/catlist/1999/bimod-biclosed (1236 words)

	Publicaciones (artículos)
		Algebra 23 (1995), no. 14, 5395-5412 (MR 96m:14068).
		Algebra 149 (2000), 295-303 (MR 1 762 770).
		Torres-Roldán, A. García-Casco y P. García-Sánchez, CSpace: An integrated workplace for the graphical and algebraic analysis of phase assemblages on 32-bit Wintel platform,.
	www.ugr.es /~pedro/node4.html (563 words)

	Construction of a Free Algebra (Site not responding. Last check: )
		Construct the free algebra A over the ring R and the monoid M. The ring R may be any ring, while the monoid M may be a finitely presented semigroup, monoid, or group.
		create the free algebra A over the finite field of three elements and the monoid M with two generators.
		The monoid over which the algebra A is defined.
	www.math.wisc.edu /help/magma/text600.html (146 words)

	Home Page of Recent Publications (Site not responding. Last check: )
		Certain sufficient conditions for the algebra to be noetherian and PI are determined.
		monoid, defined by the same presentation, is described.
		algebra, are principal and generated by a normal element.
	student.vub.ac.be /~efjesper/recpublic.html (2026 words)

	Category Theory
		Any monoid (and thus any group) can be seen as a category: in this case the category has only one object, and its morphisms are the elements of the monoid.
		For instance, in algebraic topology, topological spaces are related to groups (and modules, rings, etc.) in various ways (such as homology, cohomology, homotopy, K-theory).
		Even though toposes appeared in the 1960's, in the context of algebraic geometry, again from the mind of Grothendieck, it was certainly Lawvere and Tierney's (1972) elementary axiomatization of a topos which gave impetus to its attaining foundational status.
	plato.stanford.edu /entries/category-theory (11780 words)

	MathAction and Axiom AldorLanguageRestrictions
		In Axiom and in Aldor's algebra library there are currently two categories Monoid and AbelianMonoid.
		For example, there is no commutative monoid with * as the multiplication and these are needed (if one wants to look at the set of monomials in several variables as a multiplicative monoid).
		I do not question the theorectical advantage of rebuilding all algebra based on properties of operators (there is research in theory of operads which would support such a design) but I doubt their practicality, especially when the notation for the operators can only be known dynamically at run-time.
	wiki.axiom-developer.org /AldorLanguageRestrictions (1570 words)

	Amazon.com: Modern Algebra with Applications: Books: William J. Gilbert (Site not responding. Last check: )
		Modern algebra guides are often structured from the point of view of the subject’s intrinsic interest, offering only vague promises of practical applications in later courses or more sophisticated texts.
		The Polya-Burnside method of enumeration is the topic of chapter five, monoids and machines the focus of chapter seven, rings, fields, polynomial, Euclidean and quotient rings are examined in chapters eight, nine and ten.
		Modern algebra is a difficult topic due to the abstract nature of the material.
	www.amazon.com /exec/obidos/tg/detail/-/0471235431?v=glance (1425 words)

	GAP 3 Share Package "monoid"
		MONOiD is a package of GAP 3 functions for transformation monoids and related objects.
		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.
		Relations of degree n can be used to generate a monoid.
	www-groups.dcs.st-and.ac.uk /~gap/Gap3/Packages3/monoid.html (236 words)

	[No title] (Site not responding. Last check: )
		We illustrate this specifically for the monoid of all n x n matrices over a field F. If F is finite, we use this to do some enumerative combinatorics on M_n(F).
		We then study the Hecke algebra of M_n(F) and show it is isomorphic to the monoid algebra of the symmetric inverse monoid over F- generalizing the conneciton between the general linear group and the symmetric group.
		We indicate how this all generalizes to a large class of monoids called monoids of Lie Type.
	www.math.technion.ac.il /~techm/20040425141520040425mar (134 words)

	Wiley::Post-Modern Algebra
		The book broadens the field of study to include algebraic structures and methods used in current and emerging mathematical research, and describes the powerful yet subtle techniques of universal algebra and category theory.
		Classical algebraic areas of groups, rings, fields, and vector spaces are bolstered by such topics as ordered sets, monoids, monoid actions, quasigroups, loops, lattices, Boolean algebras, categories, and Heyting algebras.
		It is also an extremely useful resource for professionals and researchers in many areas who must tackle abstract, linear, or universal algebra in the course of their work.
	www.wiley.com /cda/product/0,,0471127388\|desc\|2715,00.html (320 words)

	[No title]
		To merely state the conjectures correctly requires much of the machinery of class field theory, the structure theory of algebraic groups, the representation theory of real and p-adic groups, and (at least) the language of algebraic geometry.
		A "monoid", recall, is a set with a binary associative product and unit.
		So, we have two closely related monoids: (N,+,0) and (N,x,1) Given a monoid, we can form something called its "monoid algebra" by taking formal complex linear combinations of monoid elements.
	math.ucr.edu /home/baez/twf_ascii/week217 (4253 words)

	Verifying an Implementation of a Polynomial Algebra ADT (Site not responding. Last check: )
		Polynomials are a free monoid algebra on the monoid of monomials and the ring of coefficients.
		This work illustrates well the capabilities of the Nuprl system; in particular, its facilities for reasoning over abstract algebraic structures such as groups, rings and modules, and for the manipulation of nested summations.
		A write-up of this work can be found in a chapter of my thesis, which will be available as a Cornell Tech-Report in the next week or two.
	www.cs.cornell.edu /NuPrl/PRLSeminar/PRLSeminar94_95/Jackson/Nov29.html (176 words)

	Universität Osnabrück - Institut für Mathematik - Algebraische Geometrie/Kommutative Algebra
		Algebraic shifting and exterior and symmetric algebra methods (Abstract)
		Commutative algebra arising from the ADG conjectures (Abstract)
		Papers based on lectures delivered at the international conference on commutative algebra and algebraic geometry, Messina, Italy, June 16-20, 1999.
	www.mathematik.uni-osnabrueck.de /preprints/kommalg.shtml (519 words)

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