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Topic: Module algebra

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	PlanetMath: algebra (module)
		Most of the important algebras in mathematics belong to one or the other of two classes: the unital associative algebras, and the Lie algebras.
		Any unital associative algebra is an algebra in the sense of djao (a sense which is also used by Lang in his book Algebra (Springer-Verlag)).
		This is version 2 of algebra (module), born on 2002-12-31, modified 2005-04-14.
	planetmath.org /encyclopedia/AlgebraModule.html (215 words)

	PlanetMath: algebra
		This is version 10 of algebra, born on 2001-10-19, modified 2006-07-31.
		Object id is 353, canonical name is Algebra.
		While this entry may be technically correct, I still woulden't know what algebra was by reading it ;) May I suggest a short history of the invention of algebra, as well something to to tune of "a system to manipulate mathematical formulas"
	planetmath.org /encyclopedia/Algebra.html (201 words)

	Algebra I Home
		Algebra I is our four quarter sequence that teaches a little less than two thirds of traditional Algebra I in four modules (named "Modules A thru D") mostly aligned with the
		This course differs from earlier offerings in that a high degree of accountability is immediately and continually expected of the student, while a lesser degree of mathematical rigor is imposed upon the student.
		In order for a student to pass a module, she/he must pass each test within that module with a score of 80% or higher on each tested concept.
	mysite.verizon.net /tajames1000/algebra-I/algebra-I.html (205 words)

	Modules over a General Algebra
		A left-module over an algebra A is a vector space V together with a bilinear map A x V to V. A right-module over A is a vector space V together with a bilinear map V x A to V. Magma provides functionality for both kinds of modules.
		Given a sequence of algebra modules Q (all defined over the same algebra, and all left (respectively right) modules), returns the module M that is the direct sum of the modules in Q. Furthermore, two sequences of mappings are returned.
		Given an algebra module M over the algebra A, and a subalgebra B of A, return M as a B-module.
	www.math.lsu.edu /magma/text918.htm (425 words)

	Projective module - Wikipedia, the free encyclopedia
		In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module (that is, a module with basis vectors).
		If there is some notion of "localization" which can be carried over to modules, such as is given at localization of a ring, one can define locally free modules, and the projective modules then typically coincide with the locally free ones.
		Submodules of projective modules need not be projective; a ring R for which every submodule of a projective left module is projective is called left hereditary.
	en.wikipedia.org /wiki/Projective_module (1057 words)

	UCC Book of Modules, 2006/2007: Mathematics
		Module Content: Algebraic manipulations and equations; Powers; Scientific notation; Formulation of verbal problems; Graphs and their interpretation; Trigonometric functions and their inverse functions; Co-ordinate geometry of the line and circle; Exponentials and logarithms, Physical applications.
		Module Objective: To develop students' capacity to visualise and work with surfaces and regions in 3-dimensional space, and develop the theory and applications of functions defined in the plane and in space.
		Module Content: A study of the interaction of topological and algebraic structures, of fundamental importance in contemporary mathematics and its applications to physics.
	www.ucc.ie /admin/registrar/modules/descriptions/page046.html (5051 words)

	Algebra (Site not responding. Last check: 2007-10-12)
		College algebra is considered a basic mathematics course.
		Certain topics usually associated with algebra, such as logarithms, have been covered elsewhere; others will be covered in modules on spreadsheets, geometry, statistics and calculus.
		This module concludes with a summative quiz, so be sure you have mastered the material.
	www.bsu.edu /web/jcflowers1/rlo/160mod10algebra.htm (164 words)

	[ref] 60 Algebras
		An algebra module is a vector space together with an action of an algebra.
		So a module over an algebra is constructed by giving generators of a vector space, and a function for calculating the action of algebra elements on elements of the vector space.
		This must be a function of two arguments; the first argument is the algebra element, and the second argument is a vector; it outputs the result of applying the algebra element to the vector.
	www-groups.dcs.st-and.ac.uk /~gap/Manuals/doc/htm/ref/CHAP060.htm (5050 words)

	[No title]
		We prove that the homotopy theory and Andre-Quillen cohomology of E1 simplicial algebras are equivalent to the homotopy theory and Andre-Quillen cohomology of E1 differential graded algebras.
		These categories of A-modules have suspension functors that refine the suspension in the category of simplicial k-modules an* d in the category of differential graded k-modules (where suspension is the shift fu *nctor).
		In the module case, similar observations apply with FA and FN(A) playing the roles of E and C. We have already shown in both the algebra and module contexts that the nor- malization functor N preserves fibrations and weak equivalences.
	hopf.math.purdue.edu /Mandell/mandell-taq.txt (12672 words)

	A Reflective Module Algebra with Applications to the Maude Language
		Module operations belong to the metalevel of the logic in question, that is, they can be seen as functions taking modules and returning other modules as results.
		As a first step towards a generic module algebra in a framework logic such as rewriting logic, we have defined an extensible module algebra for rewriting logic itself, and have realized that design using the reflective capabilities of the rewriting logic language Maude.
		For example, we explain in some detail how the transformation from object-oriented modules to system modules, which was originally proposed by Meseguer, is integrated with the overall module algebra; we explain also in some detail the renaming of modules, and the instantiation of parameterized modules.
	maude.cs.uiuc.edu /papers/abstract/Dmodalg_1999.html (1539 words)

	Maude's Module Algebra (Site not responding. Last check: 2007-10-12)
		We have followed this approach and we have used the specification of such a module algebra as its implementation, including a user interface and an execution environment for it.
		The high level at which the specification of the module algebra has been given makes this approach particularly attractive when compared to conventional implementations, because of its shorter development time and the greater flexibility, maintainability, and extensibility that it affords.
		We explain the general principles of the reflective design of the module algebra and explain the categorical semantics of parameterized theories, modules and views and their instantiation, and the reflective algebraic specification of the different module and view operations.
	maude.cs.uiuc.edu /papers/abstract/DMmodalg_2000.html (167 words)

	Springer Online Reference Works
		The endomorphism ring of a tilting module over a finite-dimensional hereditary algebra (cf.
		Riedtmann classification), is a tilting module, sometimes called APR-tilting module.
		The latter case is equivalent to the fact that the tilting module contains non-zero pre-projective and pre-injective direct summands simultaneously.
	eom.springer.de /t/t130100.htm (443 words)

	Algebra Through Modeling With The TI-83 -- Step-By-Step Instructions
		We estimate that the work for this module will take participating teachers an average of about 25 hours to complete with a range of about 20 to 30 hours.
		That should easily be possible even when you are teaching if you set aside three or four hours each week to work on the module.
		Those of you enrolled for continuing education credit will be sent feedback on the three assignments that you were required to submit.
	mtl.math.uiuc.edu /modules/algebra/what_to_do.htm (1026 words)

	Seminario de Algebra: 2004
		In particular we show that the central H-invariant elements of the Martindale ring of quotients of a module algebra form a von Neumann regular and self-injective ring whenever A is semiprime.
		Generalized Weyl algebras, as defined by V. V. Bavula [St. Petersburgh Math. J., 1993], are a family of algebras containing both some classical objects (enveloping algebras and their prime quotients, Weyl algebras, invariant sub-algebras, ...) and their quantum analogues.
		In particular one has that studying polynomial identities with involution for this algebra one may work with the analogs of the transpose and the symplectic involutions only, as it is the case with the full matrix algebra.
	mate.dm.uba.ar /~aldoc9/SA/sa-2004.html (638 words)

	MATHEMATICS II INFORMATION SHEET
		You will receive two sets of notes for this module: a short set of notes entitled Nuts and bolts for MAM200W (this is the material on foundations) and a more substantial set of notes on Linear Algebra.
		Your class record for this module is the average of your marks for the two class tests.
		Your final mark for the module is calculated in one of two ways; either the class record counts 20% and the final examination 80% or the class record counts 40% and the final examination 60 %, whichever is to your advantage.
	www.mth.uct.ac.za /Courses/MAM200W/2LA/2lainfo.html (928 words)

	Module algebra.mx (Site not responding. Last check: 2007-10-12)
		An advantage of using the exact X100 relational algebra is that, later on, students will be able to execute real X100 queries using the experimental X100 system.
		Apart from their use of reducing the columns of a table, projections are thus useful for computing all kinds of (complex) expressions.
		Notice that as opposed to a project in the strict relational algebra sense, the X100 project does not perform any duplicate elimination; hence, the result of the X100 project is not necessarily a set of tuples, but may rather be a multi-set of tuples.
	homepages.cwi.nl /~manegold/teaching/DBtech2004/practicum/algebra.html (1571 words)

	An Extensible Module Algebra for Maude (Site not responding. Last check: 2007-10-12)
		The fact that rewriting logic and Maude are reflective, so that rewriting logic specifications can be manipulated as terms at the metalevel, opens up the possibility of defining an algebra of module composition and transformation operations within the logic.
		This makes such a module algebra easily modifiable and extensible, enables the implementation of language extensions within Maude, and allows formal reasoning about the module operations themselves.
		In this paper we discuss in detail the Maude implementation of a specific choice of operations for a module algebra of this type, supporting module operations in the Clear/OBJ tradition as well as the transformation of object-oriented modules into system modules.
	maude.cs.uiuc.edu /papers/abstract/DMmodalg_1998.html (120 words)

	algebra: module that defines the core of the MIL algebra. (Site not responding. Last check: 2007-10-12)
		algebra: module that defines the core of the MIL algebra.
		Since each algebraic operands may apply different strategies, according to different status in its operand properties, each algebraic operator may have different propagation rules with these different situations as conditions.
		With the property propagation rules in hand, for each algebraic operator, split out for each different algorithmic strategy in each operator, it is a small step to a full cost model.
	monetdb.cwi.nl /TechDocs/Core/Modules/algebra/index.html (4184 words)

	Python linear algebra module -- requesting comments on interface
		Hi, I'm in the process of writing a Python linear algebra module.
		Since one of the module's targeted applications is for 3D applications, I think there should be some specific support for applying the Matrix-vector product operation to a sequence of vectors instead of only one at a time -- and it should be possible to optimize the module's code for this common case.
		Somewhere on the python site is a reference to the 'Academic License' which I believe says about this much (as does the Python license) and which is compatible with possible donation to PSF.
	www.codecomments.com /message598885.html (1675 words)

	Penn State M.T.O. Item Description and Download
		These files are animations used in a College Algebra module on functions and composite functions.
		Flash algebra self check quizzes are available in a separate download.
		Other Uses: This could be used in algebra courses or as a refresher module in more advanced math or science courses.
	tlt.its.psu.edu /mto/algebra/functionfla.html (359 words)

	Modules over a General Algebra (Site not responding. Last check: 2007-10-12)
		This section describes the functionality for modules over general algebras in Magma.
		A left-module over an algebra A is a module M together with a bilinear map A x M to M. A right-module over A is a module M together with a bilinear map M x A to M. Magma provides functionality for both kinds of modules.
		Construct the quotient module of M by the submodule S of M, the submodule containing the elements in the sequence S or the elements e1,..., en.
	magma.maths.usyd.edu.au /magma/htmlhelp/text959.htm (484 words)

	module - OneLook Dictionary Search
		Module : eyefortransport e-commerce transportation glossary [home, info]
		Phrases that include module: lunar excursion module, single in-line memory module, dual in-line memory module, service module, free module, more...
		Words similar to module: faculty, component, mental faculty, unit, more...
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=module (364 words)

	Module: Linear Algebra II
		· To consolidate material in Linear Algebra I · To familiarise student with eigen problems and their applications · To encourage use of computer packages (e.g.
		Assume that a 7.5 credit module load represents approximately 112.5 hours' work, which includes all teaching, in-course assignments, laboratory work or other specialised training and an estimated private learning time associated with the module.
		However, the following may be helpful and is close in spirit to the material.
	www.dcu.ie /registry/module_contents.php?function=2&subcode=MS104 (208 words)

	XHTML Document Profile Requirements
		Note: Preferences for modules and attribute values etc. need to be treated as part of formalization of client capabilities and personal preferences, rather the document profiles which provide a declarative description of a group of documents.
		One possible approach is to provide an algebra for adding and subtracting modules as a basis for describing document profiles, where the document syntax is defined by reference to a DTD or XML schema specifying the combined effect of the modules.
		The way profile information is structured in the profile document should be such that the effort is minimized to map between a profile document and a content negotiation session using the same data.
	www.w3.org /TR/1999/WD-xhtml-prof-req-19990906 (3724 words)

	Theory Module (Isabelle2005: October 2005)
		x = x" shows "module R M" by (auto intro: module.intro cring.axioms abelian_group.axioms module_axioms.intro prems) lemma algebraI: includes struct R + struct M assumes R_cring: "cring R" and M_cring: "cring M" and smult_closed: "!!a x.
		qed lemma (in algebra) smult_r_null [simp]: "a ∈ carrier R ==> a \
		algebra R M; a ∈ carrier R; x ∈ carrier M ] ==> a \
	www.cl.cam.ac.uk /Research/HVG/Isabelle/dist/library/HOL/HOL-Algebra/Module.html (736 words)

	Functions for Polynomial Algebra and Module Generators
		B is sequence of length l of booleans such that for 1 <= i <= l, B[i] is true iff L[i] is in the module M. V is a sequence of length l consisting of sequences of length r and consisting of polynomials in the polynomial ring T=K[t_1,..., t_r].
		Again, this function is most often used with an invariant ring: P is the sequence of primary invariants, S is the sequence of secondary invariants, and L is a sequence of general invariants which one wishes to express in terms of the module generators S over the algebra generated by P.
		Also, if one wishes to just test for membership in the algebra A=K[p_1,..., p_k], the sequence [R!1] should be passed for S. HomogeneousModuleTestBasis(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
	www.umich.edu /~gpcc/scs/magma/text854.htm (409 words)

	Module 2 Algebra
		This chapter covers the laws used for solving algebraic equations.
		As a result, one should be very familiar with the basic laws that govern the use of real numbers.
		Most of these laws are covered under the general area called Algebra.
	www.tpub.com /doemathematics/mathematics38.htm (381 words)

	VideoText Algebra - Module D - VHS
		VideoText Algebra is also available in DVD format.
		Jay L. Wile, author of the Apologia science curriculum, calls this "the best" algebra program he's seen....
		It doesn't just teach you how to manipulate algebraic formulas to get correct answers on standardized tests.
	www.sonlight.com /RM704R.html (260 words)

	OptimaNumerics: Intelligent Performance
		Performance of the linear algebra routines used is a critical factor affecting ultimately performance of your application.
		OptimaNumerics Parallel Linear Algebra Module routines are accessible from your C, C++ or Fortran applications, and is supported on platforms including:
		Contact This email address is being protected from spam bots, you need Javascript enabled to view it, or see OptimaNumerics Linear Algebra Module for more details.
	www.optimanumerics.com /index.php?option=com_content&task=view&id=22&I... (304 words)

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