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Topic: Associative rings

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	13: Commutative rings and algebras
		Of particular interest are several classes of rings of interest in number theory, field theory, algebraic geometry, and related areas; however, other classes of rings arise, and a rich structure theory arises to analyze commutative rings in general, using the concepts of ideals, localizations, and homological algebra.
		Conversely, the study of a ring is often focused by the examination of related fields, such as the quotients by each of the maximal ideals, or, in the case of integral domains, by the quotient field.
		Rings associated to group a group G shed light on the structure of G, particular rings of invariants k(V)^G (given a group action on a vector space V), cohomology rings H^(G,Z), group rings* Z[G], and representation rings R(G).
	www.math.niu.edu /~rusin/known-math/index/13-XX.html (0 words)

	PlanetMath: examples of rings
		This is an example of a Boolean ring.
		A special case of Example 6 under the section on non-commutative rings is the ring of endomorphisms over a ring
		This is version 35 of examples of rings, born on 2005-02-06, modified 2006-10-01.
	planetmath.org /encyclopedia/ExampleOfRings.html (197 words)

	16: Associative rings and algebras
		This includes the study of matrix rings, division rings such as the quaternions, and rings of importance in group theory.
		Solving polynomial equations in the ring of quaternions; passing to extension rings.
		Pointer and citation to solving quadratic equations in the ring of quaternions.
	www.math.niu.edu /~rusin/known-math/index/16-XX.html (541 words)

	Springer Online Reference Works
		An alternative ring is a ring in which every two elements generate an associative subring; an alternative algebra is a (linear) algebra that is an alternative ring.
		The difference between associative rings and alternative rings is also strongly manifested by the fact that alternative rings contain various kinds of nilpotency, since the product of elements may be zero or non-zero, depending on the placement of the parentheses.
		The theory that establishes sufficient criteria of local nilpotency of an alternative ring is completely parallel to the corresponding theory for associative rings.
	eom.springer.de /a/a012090.htm (0 words)

	PlanetMath: power-associative algebra
		, since the associator is trilinear (linear in each of the three coordinates).
		A theorem, due to A. Albert, states that any finite power-associative division algebra over the integers of characteristic not equal to 2, 3, or 5 is a field.
		This is a generalization of the Wedderburn's Theorem on finite division rings.
	planetmath.org /encyclopedia/PowerAssociativeAlgebra.html (133 words)

	Ring (mathematics) - Wikipedia, the free encyclopedia
		A ring is a generalization of the integers.
		Similarly, the requirement for the ring multiplication to be associative is sometimes dropped, and rings in which the associative law holds are called associative rings.
		Given a ring R and an ideal I of R, the quotient ring (or factor ring) R/I is the set of cosets of I together with the operations
	en.wikipedia.org /wiki/Ring_(mathematics) (1394 words)

	Fast Breaking Comment by Wallace S. Martindale
		An "associative ring" is a set of elements with two binary operations, called "addition" and "multiplication," which satisfies several basic and natural axioms (e.g.
		From the standpoint of "noncommutative" ring theory the prototype example is the set of all linear transformations of a (possibly infinite dimensional) vector space.
		An associative ring R may be turned into a "Lie ring" by keeping the same addition but defining a new multiplication: [x,y] = xy - yx.
	www.esi-topics.com /fbp/2003/october03-WallaceSMartindale.html (742 words)

	Subject: 16-xx ASSOCIATIVE RINGS AND ALGEBRAS (Site not responding. Last check: 2007-11-02)
		Note on separable extensions of noncomutative rings, 1988.
		On bicommutators of modules over H‐separable extension rings, 1990.
		On H‐separable extensions of primitive rings II, 1988.
	eprints.math.sci.hokudai.ac.jp /view/subjects/16-xx.html (0 words)

	Le résultat de votre recherche (Site not responding. Last check: 2007-11-02)
		This book is the first to present a complete theory of filtrations on associative rings, combining techniques stemming from number theory related to valuations, with facts originating in the study of rings of differential operators on varieties.\par It is divided into four chapters, each of which is subdivided into sections.
		The case where the associated graded ring of a filtered simple Artinian ring is a semiprime P.I. ring is reduced to the prime case, by using microlocalization; without P.I. hypothesis an extra assumption is necessary in order to arrive at the same conclusion (see resp.
		Zariski rings with noetherian Rees ring and with commutative associated graded ring are investigated.
	www.math.jussieu.fr /~keller/semalg/li.html (2114 words)

	The Math Forum - Math Library - Rings/Ideals (Site not responding. Last check: 2007-11-02)
		Commutative rings are sets like the set of integers, allowing addition and (commutative) multiplication.
		Of particular interest are several classes of rings of interest in number theory, field theory, and related areas; however, other classes of rings arise, and a rich structure theory arises to analyze commutative rings in general, using the concepts of ideals, localizations, and homological algebra.
		One of its main research interests lies in near-rings: generalised rings that might generally be described as rings (N,+,*) where the addition is not necessarily abelian and only one distributive law...more>>
	mathforum.org /library/topics/rings_ideals (685 words)

	Kurosh's Introduction to "Lectures on general algebra"
		How great, and sometimes decisive, the impact of this modern algebra was on the development of many domains of mathematics, among which we mention, in the first instance, topology and functional analysis, is common knowledge.
		During these decades, the older branches of general algebra - the theory of fields and of associative and associative-commutative rings, to which van der Waerden's book was mainly devoted - have undergone far-reaching changes.
		At the same time, the theory of rings became more and more a theory of non-associative rings, incorporating as a constituent part the theory of Lie rings and Lie algebras.
	www-groups.dcs.st-and.ac.uk /~history/Extras/Kurosh_algebra.html (1428 words)

	George M. Bergman -- publications and preprints
		Rings with fixed-point-free group actions (with I. Isaacs), Proc.
		Hereditarily and cohereditarily projective modules, pp.29-62 in Ring Theory (proceedings of a conference held in Park City, UT March 2-6 1971), Robert Gordon ed., Academic Press 1972.
		Hereditary commutative rings, and centres of hereditary rings, Proc.
	math.berkeley.edu /~gbergman/papers (1286 words)

	GAP (Circle) - Chapter 1: Introduction
		Let R be an associative ring, not necessarily with one.
		The group of all invertible elements of this monoid is called the adjoint group of R and is denoted by R^*.
		Sysak give a survey of results on adjoint groups of radical rings, including such topics as subgroups of the adjoint group; nilpotent groups which are isomorphic to the adjoint group of some radical ring; adjoint groups of finite nilpotent $p$-algebras.
	www-groups.dcs.st-and.ac.uk /~gap/Manuals/pkg/circle/doc/chap1.html (489 words)

	Commutative Ring Theory Seminar, Fall 2003 (Site not responding. Last check: 2007-11-02)
		The goal of the Commutative Ring Theory Seminar is to encourage interaction among members of the department whose interests include commutative ring theory.
		Relative cohomology defined for left modules over associative rings of finite Gorenstein projective dimension is shown to be related to Tate cohomology and Ext functor by a long exact sequence.
		As an application, we prove that a local ring R of characteristic p is Gorenstein if and only if some power of its Frobenius endomorphism has finite Gorenstein dimension.
	www.math.uiuc.edu /~ssather/MATH/crt_fa03.html (644 words)

	Small Rings
		We are being fairly arbitrary with what is a "nice" description of a ring, but these seem to fit most people's description of "nice" rings.
		Of particular interest are his technical report Numbers of small rings (ps-file, middle of the page) and this chart on the number of rings of prime-power order.
		The number of rings of size 0, 1, 2, 3, 4, 5, etc. forms the sequence 0, 1, 2, 2, 11, 2, etc., also known as sequence number A037234 from Neil Sloane's On-line Encyclopedia of Integer Sequences.
	home.wlu.edu /~dresdeng/smallrings (557 words)

	AMCA: Decompositions of associative rings by Vladimir Kirichenko (Site not responding. Last check: 2007-11-02)
		A ring is called decomposable if it is a direct product of two rings, otherwise the ring is indecomposable.
		A ring A is called a finitely decomposable ring (FD-ring) if it is a finite direct product of indecomposable rings.
		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/f/e/45.htm (184 words)

	Cogroups and Co-Rings in Categories of Associative Rings (Mathematical Surveys and Monographs) by George M. Bergman, ...
		All such functors from associative rings over a fixed ring $R$ to each of the categories of abelian groups, associative rings, Lie rings, and to several others are determined.
		Rings, Modules and Algebras in Stable Homotopy The...
		Fixed Rings of Finite Automorphism Groups of Assoc...
	www.bookfinder4u.com /detail/0821804952.html (386 words)

	Bulletin of the American Mathematical Society
		A. Grishin, A variety of associative rings is not Spechtian, Uspekhi Mat.
		I. Kaplansky, Rings with a polynomial identity, Bull.
		W. Schelter, Noncommutative affine PI rings are catenary, J. Algebra 51 (1978), 12-18.
	www.ams.org /bull/2006-43-04/S0273-0979-06-01106-2 (0 words)

	Raghavendran: Finite associative rings
		[1] Properties of Rings with a Finite Number of Zero Divisors, Math.
		[2] Properties of Rings with a Finite Number of Zero Divisors II, Math.
		[4] On "Properties of Rings with a Finite Number of Zero Divisors", Math.
	math-doc.ujf-grenoble.fr /numdam-bin/item?id=CM_1969__21_2_195_0 (48 words)

	Sergio Lopez's research interests (Site not responding. Last check: 2007-11-02)
		My research revolves mostly around the theory of modules over arbitrary associative rings with unity.
		A module M is said to be weakly injective if any finitely generated submodule of the injective hull E(M) of M is contained in a submodule X of E(M) which is isomorphic to M. The study of weak injectivity has connections with the study of QI-rings, semiprime Goldie rings, q.f.d.
		Algebraic Coding Theory continues to be an interesting topic for me. A paper on cyclic codes over the integers modulo p^n, written with Pramod Kanwar has recently been accepted for publication by Finite Fields and their applications.
	www.math.ohiou.edu /~slopez/research.htm (217 words)

	AMCA: Some extremal varieties of associative algebras by Elena Kireeva
		The class of all associative F-algebras satisfying a given set of identities is called a variety.
		We refer to [1], [4], [5] and [8] for the terminology and basic facts concerning varieties of associative algebras and polynomial identities.
		is a minimal variety of associative F-algebras whose relatively free algebras of countable infinite rank contain non-finitely generated T-spaces.
	at.yorku.ca /c/a/l/i/03.htm (474 words)

	Computational algebraic techniques using computers and representation theory (Site not responding. Last check: 2007-11-02)
		Other common algebras are the alternative algebras, Jordan algebras, Bernstein algebra, genetic algebras, Malcev algebras, and of course, associative algebras.
		Our task is to invent algorithms and techniques which enable problems to be processed by the computers.
		Rings with (a,b,c)=(a,c,b) and (a,[b,c],d) = 0; a Case Study Using Albert, International Journal of Computers in Math 49 (1993), 19-27, (with D. Jacobs of Clemson S.C. and E. Kleinfeld of Iowa City, Iowa).
	orion.math.iastate.edu /research/nonassocrings/compalg.html (476 words)

	Rings Marketing
		Four leading agencies have combined their marketing experience to offer brands a unique, 360 degree full service solution
		Rings Marketing is a joint venture between Sportsworld, brandRapport, b-focused and Spring Worldwide.
		By combining their extensive experience, the company is in a unique position within the UK to provide an independent and experienced consulting service, focused on delivering a return on investment for its clients.
	www.ringsmarketing.com (0 words)

	CARL FAITH:Professor Emeritus, Mathematics, Rutgers University
		(1) The Structure of commutative and non-commutative associative rings(=ring theory) and their modules (= module theory), field theory, theory ofequations, Galois theory for commutative and skew fields, and Ore domains,rings of polynomials, linear and matrix rings, simple, prime or semiprimeGoldie rings, ascending chain conditions on annihilator or irreducible ideals, Noetherian rings and coherent rings.
		(2) Quotient Rings: maximal and classical quotient rings, especially ringswith self-injective quotient rings.
		(5) Commutativity theorems and the generation of rings by certain elements,e.g., nth powers, or conjugates of certain elements, invariant subrings.
	www.phoenix-designs.com /carlfaith/index.htm (137 words)

	16-XX
		16Kxx Division rings and semisimple Artin rings, see also {12E15, 15A30}
		16Sxx Rings and algebras arising under various constructions
		16Uxx Conditions on elements (including elements of matrix rings, etc.)
	www.ma.hw.ac.uk /~chris/MR/16-XX.html (0 words)

	A SOMONAR Photo Album (Site not responding. Last check: 2007-11-02)
		The Department of Mathematics of the University of Colorado at Colorado Springs hosted the Symposium on Modules over Nonunital Associative Rings (SOMONAR) on June 1-3, 1997.
		One potentially important outgrowth of this symposium is the creation of WOMONAR, the Website Of Modules Over Nonunital Associative Rings.
		In addition to the formal mathematics there were ample occasions to socialize, relax, and sight-see in the beautiful Colorado Springs area.
	darkwing.uoregon.edu /~anderson/album/albumg.html (498 words)

	Conference Papers of Dr.W.B.Vasantha Kandasamy (Site not responding. Last check: 2007-11-02)
		A note on the modular semi group ring of a finite idempotent semigroup
		Commutator and Associator of a new class of loops
		Study of Health Hazards associated with handling of solid wastes using neural networks
	mat.iitm.ac.in /~wbv/clist.htm (1700 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		(Commutative rings and algebras; here there is a fine line to tread between commutative algebras and algebraic geometry; algebraic geometry is not a topic that will be dealt with in this Handbook; a separate Handbook on that topic is under consideration)
		Commutative and associative rings and algebras with extra structure
		For a more detailed plan, the reader is reffered to the Outline of the Series following the Preface.
	www1.elsevier.com /homepage/saj/523281/preface.htm (820 words)

	On non-Spechtianness of the variety of associative rings that satisfy the identity $x^{32} = 0$
		On non-Spechtianness of the variety of associative rings that satisfy the identity $x^{32} = 0$
		In this paper we construct examples of $T$-spaces and $T$-ideals over a field of characteristic 2, which do not have the finite basis property.
		Electronic Research Announcements of the AMS Home page
	www.emis.de /journals/ERA-AMS/2000-01-007/2000-01-007.html (0 words)

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