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Topic: Ring algebra

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	Ring (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have similar (but not identical) properties to those familiar from the integers.
		A ring (in the categorical sense) is commutative iff it is equal to its opposite ring.
		The split-complex plane D is a ring useful in modern physics and is a subring of the tessarines.
	en.wikipedia.org /wiki/Ring_(algebra) (1102 words)

	Algebra (ring theory) - Wikipedia, the free encyclopedia
		In ring theory, an algebra over a base ring is a generalization of the concept of associative algebra.
		An R-algebra is a ring S together with a ring homomorphism from R to the center of S.
		The notion of R-algebra generalizes that of an associative algebra: if K is a field, then any associative algebra over K is a K-algebra and vice-versa.
	en.wikipedia.org /wiki/Algebra_(ring_theory) (144 words)

	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 (211 words)

	Ring (mathematics) - FreeEncyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have similar properties to those familiar from the integers.
		The set of all invertible elements in a ring is closed under multiplication * and therefore forms a group, the group of units of the ring.
		Given a ring R and and ideal I, the factor ring is the set of cosets of R/I together with operations gI+hI=(g+h)I and (gI)(hI)=ghI.
	openproxy.ath.cx /ri/Ring_(algebra).html (549 words)

	NTU Info Centre: Commutative ring (Site not responding. Last check: 2007-11-06)
		In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation obeys the commutative law.
		Given a commutative ring R and an ideal I of R, the factor ring R/I is the set of cosets of I together with the operations (a+I)+(b+I)=(a+b)+I and (a+I)(b+I)=ab+I.
		The outer structure of a commutative ring is determined by considering linear algebra over that ring, i.e., by investigating the theory of its modules.
	www.nowtryus.com /article:Commutative_ring (835 words)

	[No title]
		algebraic structure in which addition and multiplication are defined and have similar properties to those familiar from the integers.
		The split-complex plane D is a ring useful in modern physics.
		The centre of a ring R is the set of elements of R that commute with every element of R; that is, c lies in the centre if cr=rc for every r in R.
	en-cyclopedia.com /wiki/Ring_(mathematics) (972 words)

	Search Results for Ring
		Another major topic in ring theory is the study of local rings, that is rings having a unique maximal ideal, and they are used in the study of local properties of algebraic varieties.
		A "Boolean-like" ring is a commutative ring H with unit element such that a + a = 0 for all a in H and ab(a + b + ab) = ab for any two elements a, b of H. Gelfand
		Ring theory in its own right was born together with an early hint of the axiomatic method which was to dominate algebra in the 20thCentury.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Ring&CONTEXT=1 (3806 words)

	PlanetMath: algebra
		In this definition, all rings are assumed to be rings with identity and all ring homomorphisms are assumed to be unital.
		This is version 9 of algebra, born on 2001-10-19, modified 2005-04-10.
		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 (199 words)

	[No title]
		Manufacturing all R-algebras as quotients of polynomial rings over R. Manufacturing \Q as a quotient of a polynomial ring over \Z. Manufacturing localizations in general.
		Algebra finitely generated as a module is integral.
		Relation between the blowup algebra and the associated graded algebra.
	cr.yp.to /1998-515/inclass.html (1124 words)

	class rings (Site not responding. Last check: 2007-11-06)
		A subset I of the ring R is a left ideal of R...
		See live article Ring homomorphism In abstract algebra, a ring homomorphism is a function between two rings which respects the operations of addition and multiplication.
		Ring homomorphisms Let R and S be ringss and let f be a ring homomorphism from R to S. If 0S is...
	www.byglrb.com /jewelry/class+rings (1438 words)

	CARL FAITH:Professor Emeritus, Mathematics, Rutgers University
		Injective cogenerator rings and a theorem of Tachikawa, I, Proc.
		On hereditary rings and Boyle's conjecture, Archiv der Mathematik, 27 (1976), 113-119.
		Injective cogenerator rings and a theorem of Tachikawa, II, Proc.
	www.phoenix-designs.com /carlfaith/pub.htm (1522 words)

	Jonathan S. Golan, Publications
		The lattice of torsion theories associated with a ring, in F. Van Oystaeyen (ed.): Ring Theory, Proceedings of the 1977 Antwerp Conference, Marcel Dekker, New York, 1978.
		On the endomorphism ring of a module noetherian with respect to a torsion theory, Israel J. Math.
		Rings over which all torsion theories cogenerated by simple modules are jansian, Ann.
	math.haifa.ac.il /JSGOLAN/golan-papers.html (1003 words)

	[No title]
		Introduction A filtered ring is a ring R which comes equipped with a multiplicative decreasing filtration {In } of ideals: R = I0 I1 I2.
		The underlying ring of R is the filtered polynomial ring Z(p)[x] with the x-adic filtration, where x lies in filtration precisely 2(p - 1) and Z(p)is the ring of integers localized at p.
		A filtered ~-ring is a filtered ring R = (R, {In }) for which the filtration ideals In are all closed under the operations ~i for i > 0.
	hopf.math.purdue.edu /YauD/steenrod_kuhn.txt (5800 words)

	The Algebra of an Invariant Ring and Algebraic Relations (Site not responding. Last check: 2007-11-06)
		Then R is generated as an algebra over K by the primary invariants f_1,..., f_n and the irreducible secondary invariants h_1,..., h_r.
		Thus R can be regarded as an homomorphic image of A and finding the algebraic relations between these (algebra) generators of R yields a presentation of R as a quotient of a polynomial algebra.
		Given an invariant ring R=K[V]^G, return the algebra corresponding to the primary invariants of R as a graded polynomial ring (with the weights corresponding to the degrees of the primary invariants).
	magma.maths.usyd.edu.au /magma/htmlhelp/text962.htm (561 words)

	Algebra
		The document Graduate Study in Algebra outlines the general areas of algebra studied here and describes the advanced undergraduate and graduate courses that are offered regularly.
		Commutative algebra, polynomials in several variables, homological algebra, ring theory.
		Model theory and algebra; stability theory, model theory of groups and fields with applications, differential fields.
	www.math.uiuc.edu /GraduateProgram/researchmath/algebra.html (251 words)

	Ring (mathematics) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		In ring theory, a branch of abstract algebra, a ring is an algebraic structure in which addition and multiplication are defined and have similar properties to those familiar from the integers.
		is not among the ring axioms listed above; rings that satisfy this law (such as the ring of integers) are called commutative rings.
		Since any ring is both a left and right module over itself, it is possible to construct the tensor product of R over a ring S with another ring T to get another ring.
	www.peacelink.de /index.php?title=Ring_(algebra)&redirect=no (850 words)

	Publications of Michel Van den Bergh
		Motivated by their work on classical rings of invariants, Levasseur and Stafford asked whether the ring of invariants under G of the symmetric algebra of W has a simple ring of differential operators.
		In the language of non-commutative algebraic geometry this amounts to a generic description of ``curves'' of degree $d$ in a projective quantum plane.
		Roughly speaking and by analogy with the commutative situation, the category of graded modules modulo torsion over a noncommutative graded ring of quadratic, respectively cubic growth should be thought of as the noncommutative analogue of a projective curve, respectively surface.
	alpha.uhasselt.be /Research/Algebra/Publications/michel_pub.html (4222 words)

	Passman's Publications (Site not responding. Last check: 2007-11-06)
		A mechanism for describing ideals in group rings, Ring Theory, Proceedings of Conference on Noncommutative Rings, Marcel Dekker, New York (1977), 63-69.
		Algebraic analogs of the Connes spectrum, (with S. Montgomery) J. Algebra 115 (1988), 92-124.
		X-inner automorphisms of enveloping rings, (with J. Osterburg) J. Algebra 130 (1990), 277-312.
	www.math.wisc.edu /~passman/publist.html (1560 words)

	ODP: Science:Math:Algebra:Ring Theory (Site not responding. Last check: 2007-11-06)
		arXiv Front: RA Rings and Algebras - Rings and algebras section of the mathematics e-print arxiv.
		Associative Rings and Algebras - Section 16 of Dave Rusin's archive of known mathematics.
		Nonassociative Rings and Algebras - Section 17 in Dave Rusin's Mathematical Atlas.
	beta.thesoftwarestudio.com /Science,Math,Algebra,Ring_Theory.html (133 words)

	algebra definition - algebra definition (Site not responding. Last check: 2007-11-06)
		algebra (Definition) In this definition, all rings are assumed to be rings with identity and all ring homomorphisms are assumed to be unital.
		An algebra over is a ring together with a...
		Definition of Linear algebra Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations...
	algebra.rock-bottom.info /algebra-definition (584 words)

	Sarah Witherspoon: Curriculum Vitae (Site not responding. Last check: 2007-11-06)
		Abstract Algebra, Linear Algebra, and Calculus, University of Toronto, 1994-1996 and 1997-1998
		The representation ring and the centre of a Hopf algebra, Canad.
		Algebraic deformations arising from orbifolds with discrete torsion, Lie Theory Seminar, University of Wisconsin, Madison, October 15, 2002.
	www.math.tamu.edu /~sjw/cv.html (2037 words)

	[No title]
		Assert (x i j)+'(x i j)='(x j i)+'(min (x j i));Auto with algebra.
		Apply Trans with (field_inverse 1!F (ring_unit F)+'(ring_unit F))rX(x+'(min ((transpose x)::(Mmn F n n))) i j);Auto with algebra.
		Apply Trans with (min (min (Ap2 i j)))+' (min (Ap2 j i));Auto with algebra.
	www.cs.ru.nl /J.Stein/WWW/LinAlg/LinAlg/direct_sum.v (521 words)

	math answers for prentice hall
		We are currently using it to "check" homework assignment on a child struggling in Algebra 2 in High School.
		It is pretty user friendly, and, as long as you enter the problem correctly, there are no problems.
		Students struggling with all kinds of algebra problems find out that our software is a life-saver.
	www.softmath.com /algebra_stats/ring-algebra-application.html (324 words)

	Proceedings of the American Mathematical Society
		, hence is a Kerr ring in the sense that the polynomial ring
		J. Kerr, The polynomial ring over a Goldie ring need not be a Goldie ring, J. Algebra 134 (1990), 344--352, MR 91h:16042.
		------, An example of a Goldie ring whose matrix ring is not Goldie, J. Algebra 61 (1979), 590--592, MR 81b:16016.
	www.ams.org /proc/1996-124-02/S0002-9939-96-03028-6/home.html (376 words)

	Untitled Document
		In the study of group rings the knowledge of the unit group is crucial, but a complete description of the unit group in terms of generators and relations still seems out of reach, even for special classes of groups.
		Concerning the second centre and hypercentre of the unit group of the integral group ring of a periodic group G, we have that the results of Jespers and Juriaans, and Li and Parmenter [49,67] imply that these groups equal the finite conjugacy centre of the unit group.
		These components (together with non-commutative division algebras other than a totally definite quaternion algebra) are called exceptional components and the ultimate reason for excluding the matrices is that the Congruence Subgroup Theorem [6,9,106] fails for 2×2-matrices over maximal orders in the mentioned division rings.
	student.vub.ac.be /~andooms/research.htm (4659 words)

	Directory - Science: Math: Algebra: Ring Theory
		arXiv Front: RA Rings and Algebras · Rings and algebras section of the mathematics e-print arxiv.
		Associative Rings and Algebras · cached · Section 16 of Dave Rusin's archive of known mathematics.
		Nonassociative Rings and Algebras · cached · Section 17 in Dave Rusin's Mathematical Atlas.
	www.incywincy.com /default?p=800620 (92 words)

	[No title]
		User code can be compiled once the distributed algebra exists and does not need either this Makefile or this installation process.
		The steps in the process of adding this file are: \begin{enumerate} \item Find out where the algebra code lives in the lattice.
		These files are originally bootstrapped from lisp code when we build the system for the first time but they are forcibly recompiled at the end of the build so they reflect current code (just in case someone changes the spad code but does not re-cache the generated lisp).
	page.axiom-developer.org /zope/mathaction/Lattice.pamphlet (932 words)

	Ohio University Center for Ring Theory and its Applications
		The Ohio University Center for Ring Theory and its Applications seeks to further the study of ring theory and its applications by fomenting collaboration and communication with scholars from all over the world.
		We aim at promoting the study of ring theory and its applications among graduate students at Ohio University.
		We will encourage the pursuit of research on applications of ring theory to several areas; in particular, we will concentrate on the interdisciplinary efforts involved in the pursuit of Information and Coding Theory.
	www.math.ohiou.edu /~algebra/center (339 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		A N N O U N C E M E N T The Algebraic Domain Constructor DoCon Version 2.06 is available, together with its source program, on Internet at the following addresses: http://www.botik.ru/pub/local/Mechveliani/docon/2.06/ ftp.botik.ru/pub/local/Mechveliani/docon/2.06/ Version 2.06 is a bug-fix release for 2.05, 2.04.
		Categorial approach means that ------------------------------- arithmetic and some other operations are defined under the very generic assumptions: "over any Euclidean ring", over any field, and so on, the Domain Constructors are supported: Fraction, Polynomial, Residue ring, and others, that is certain set of operations are defined automatically, following the domain constructors.
		Property processing: * evaluation of certain small set of the most important algebraic property values is supported, such as Finite, IsCyclicGroup, IsMaximalIdeal, and others.
	www.haskell.org /docon/distrib/2.06/announce.txt (452 words)

	Qmaker : Science : Math : Algebra : Ring Theory search facts Qmaker : Science : Math : Algebra : Ring Theory (Site not responding. Last check: 2007-11-06)
		Rings and algebras section of the mathematics e-print arxiv.
		A webring devoted to pages concerning commutative ring theory.
		Ring Theory category powered by Free PHP ODP Script © Site Directory
	www.qmaker.se /index.php?c=Science/Math/Algebra/Ring_Theory (100 words)

	[No title]
		(** %\subsection{ extras : matrix\_algebra.v }%) ( - This is not used, but nice anyway: $n\times n$-matrices over $F$ form an algebra** (over $F$) *) Require Export Matrices.
		(Apply Trans with (sum (pointwise (uncurry (RING_comp 1!F)) (row X i) ((col x j)+'(col y j))));Auto with algebra).
		2:(Apply (!sum_of_sums n F (pointwise (uncurry (RING_comp 1!F)) (row X i) (col x j)) (pointwise (uncurry (RING_comp 1!F)) (row X i) (col y j)));Auto with algebra).
	www.cs.ru.nl /~jasper/WWW/LinAlg/extras/matrix_algebra.v (448 words)

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