Weakly finite ring
In algebra, a ring R is said to be stably finite (or weakly finite) if, for all square matrices A, B of the same size over R, AB = 1 implies BA = 1. This is a slightly stronger property for a ring than its having the invariant basis number: any nontrivial stably finite ring has IBN. Commutative rings, noetherian rings and artinian rings are stably finite. A subring of a stably finite ring and a matrix ring over a stably finite ring is stably finite. A ring satisfying Klein's nilpotence condition is stably finite.[citation needed]

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Stably finite ring - Wikipedia, the free encyclopedia
In algebra, a ring R is said to be stably finite (or weakly finite) if, for all square matrices A, B of the same size over R, AB = 1 implies BA = 1. This is a slightly ...
en.wikipedia.org/wiki/Stably_finite_ring
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On Making Rings Weakly Finite - Jstor
ON MAKING RINGS WEAKLY FINITE. PETER MALCOLMSON. ABSTRAcT. Given an associative ring R with unit we construct the largest homo- morphic image ...
www.jstor.org/stable/2042949
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Ring Theory, 83: Student Edition - Google Books Result
books.google.com/books?id=ud8MV2C76RYC&pg=PA52&lpg=PA52&dq=Weakly+finite+ring&source=bl&ots=1DEPCrx5o8&sig=rQ4Ku7c8xOellkIbHW791Mwcryg&hl=en&sa=X&ei=GaymUcSEHs307AaKl4HYDQ&ved=0CB0Q6AEwAg
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Basic Algebra: Groups, Rings, and Fields - Google Books Result
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[1305.4423] On linear groups over weakly locally finite division rings
May 20, 2013 ... Abstract: In this paper, we give the definition of {\em weakly locally finite} division rings and we show that the class of these rings strictly ...
arxiv.org/abs/1305.4423
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Free Ideal Rings and Localization in General Rings - Google Books Result
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On Weakly Finite Conductor Rings
On Weakly Finite Conductor Rings. #. Najib Mahdou*. Département de Mathématiques et Informatique, Faculté des Sciences et. Techniques Fe`s-Saıss, ...
www.tandfonline.com/doi/pdf/10.1081/AGB-200028231
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Self-injective rings and linear (weak) inverses of linear finite ...
Feb 1, 1999 ... LetR be a finite commutative ring with identity and τ be a nonnegative integer. In studying linear finite automata, one of the basic problems is ...
link.springer.com/article/10.1007%2FBF02876565
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Linear Time-Varying Systems: Algebraic-Analytic Approach - Google Books Result
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Rings Close to Regular - Google Books Result
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Weakly finite ring in science
[1305.4423] On linear groups over weakly locally finite division rings
May 20, 2013 ... Cornell University Library · We gratefully ... Mathematics > Rings and Algebras. Title: On linear groups over weakly locally finite division rings ...
The existence of free non-cyclic subgroups in weakly locally finite ...
Apr 6, 2013 ... Abstract: In this paper we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring ...
[PDF]20 May 2013 On linear groups over weakly locally finite ... - arXiv
May 20, 2013 ... §Faculty of Mathematics and Computer Science, University of Science, ... weakly locally finite division ring which is not even algebraic. Next, we ...
Weakly Finite Matrix Localizations
Department of Mathematics Wayne State University Detroit MI 48202 USA ... A ring is called weakly finite if all of its right invertible square matrices are invertible.
[PDF]WEAKLY SYMMETRIC RINGS OF DISTRIBUTIVE MODULE TYPE ...
The University of Iowa. Iowa City, Iowa 52242 ... each block of a split group algebra of finite module ... Let R be a weakly symmetric biserial ring with basic set of ...
Theory of Rings and Modules Abstracts - The Ohio State University
GARY BIRKENMEIER, University of Louisiana at Lafayette, Lafayette, LA .... - module is of finite length over its endomorphism ring. ..... Characterizations of rings over which every weakly injective is weakly projective and conversely are given.
Self-injective rings and linear (weak) inverses of linear finite ...
Feb 1, 1999 ... Self-injective rings and linear (weak) inverses of linear finite automata over ... Graduate School, University of Science and Technology of China, ...
Weakly Special Classes of Semiprime Rings - Springer
If ℳ is a special class of prime rings then the class ℳ ∞ of all finite subdirect products of rings in ℳ is shown to be weakly special. ... School of Mathematics, Statistics and Information Technology, University of Natal Pietermaritzburg, Private Bag ...
[PDF]WEAKLY PERFECT GRAPHS ARISING FROM RINGS 1 ... - IPM
or multiple edges. Also, all rings are finite commutative with non-zero identity. ... Chromatic number, Clique number, Weakly perfect graph, Finite ring. ...... M. R. Pournaki, Department of Mathematical Sciences, Sharif University of Tech- nology ...
Von Neumann regular ring - Wikipedia, the free encyclopedia
One may think of x as a "weak inverse" of a. In general x is ... The ring of affiliated operators of a finite von Neumann algebra is von Neumann regular. A Boolean ...
Books on the term Weakly finite ring
Ring Theory, 83: Student Edition
Ring Theory, 83: Student Edition
Louis H. Rowen, 1991
On the other hand, theorem 0.3.2 implies division rings do have IBN, and virtually every class of rings we shall study (Artinian rings, Noetherian rings, PI-rings, etc.) will be seen to have IBN. Weakly finite rings There is a slightly stronger ...
Lectures on Finite Fields and Galois Rings
Lectures on Finite Fields and Galois Rings
Zhe-Xian Wan, 2003
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasized. In particular, the construction of irreducible polynomials and the normal basis of finite fields are incl...
Basic Algebra: Groups, Rings, and Fields
Basic Algebra: Groups, Rings, and Fields
P. M. Cohn, 2003
It is clear that the trivial ring is weakly finite, but does not have IBN. For examples of rings with IBN that are not weakly finite, see Cohn [1966]. We remark that a ring R with the property ab = 1 => ba = 1 is also called 'weakly 1 -finite'; other ...
Finite Fields And Galois Rings
Finite Fields And Galois Rings
Zhe-Xian Wan, 2011
A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction o...
Free Ideal Rings and Localization in General Rings
Free Ideal Rings and Localization in General Rings
Paul Moritz Cohn, 2006
Show that conversely, every ring with this property is weakly M-finite. {Hint: Imitate the ... Deduce that every non-zero Weakly finite ring has UGN. 9* . Which of ... Characterize the rings all of whose homomorphic images are weakly finite. 1 1 .
Skew Fields: Theory of General Division Rings
Skew Fields: Theory of General Division Rings
Paul Moritz Cohn, 1995
A ring R is said to be weakly n-finite if any generating set of n elements of R" is free. If R is weakly n-finite for all n, it is called weakly finite . Weakly 1-finite rings are sometimes called 'von Neumann finite', 'inverse symmetric' or 'directly finite'.
Finite Geometries and Designs: Proceedings of the Second Isle of Thorns Conference 1980 (London Mathematical Society...
Finite Geometries and Designs: Proceedings of the Second Isle of Thorns Conference 1980 (London Mathematical Society...
P. J. Cameron, J. W. P. Hirschfeld and D. R. Hughes, 1981
Originally published in 1981, this collection of 33 research papers follows from a conference on the interwoven themes of finite Desarguesian spaces, Steiner systems, coding theory, group theory, block designs, generalized quadrangles, and projective planes. There is a comprehensive introduction, which aims to interest the non-specialist in the sub...
Linear Time-Varying Systems: Algebraic-Analytic Approach
Linear Time-Varying Systems: Algebraic-Analytic Approach
Henri Bourlès, Bogdan Marinescu, 2011
(2) A ring R is said to be weakly finite [79] (or stably finite [199]) if for any n ≥ 1, each generating set of n elements of Rn is free. The following conditions are equivalent ([79], Prop. 4.6.6; [199], Prop. 1.7): (i) R is weakly finite; (ii) for any n, if an ...
Organic Chemistry As a Second Language: Second Semester Topics
Organic Chemistry As a Second Language: Second Semester Topics
David R. Klein, 2011
Readers continue to turn to Klein because it enables them to better understand fundamental principles, solve problems, and focus on what they need to know to succeed. The third edition explores the major principles in the field and explains why they are relevant. It is written in a way that clearly shows the patterns in organic chemistry so that re...
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Weakly finite ring
Flat finite type ring extensions | Stacks Project Blog
Posted on August 20, 2010 by Johan.
math.columbia.edu/~dejong/wordpress/?p=753
Agol’s Virtual Haken Theorem (part 2): Agol-Groves-Manning strike back | Geometry and the imagination
Agol’s Virtual Haken Theorem (part 2): Agol-Groves-Manning strike back March 27, 2012 in Groups | Tags: height, hyperbolic Dehn surgery, hyperbolic groups, malnormal groups, quasiconvex subgroup, subgroup separation, virtually special cube complexes Today Jason Manning gave a talk on a vital ingredient in the proof of Agol’s theorem, which is a result in geometric group theory. The theorem is a joint project of Agol-Groves-Manning, and generalizes some earlier work they did a few years ago.
lamington.wordpress.com/2012/03/27/agols-virtual-haken-theorem-part-2-agol-groves-manning-strike-back/
Devinatz-Hopkins-Smith, I | Chromotopy
I’ve been chewing my way through Devinatz, Hopkins, and Smith’s landmark paper from the early 1980s, in which they prove this amazing fact that the complex cobordism spectrum is exactly the right tool for thinking about nilpotence and periodicity in stable homotopy theory, previously conjectured by Ravenel. An important maxim of homotopy theory is that Free Objects Are Complicated, which is really what sets algebraic topology apart from algebra — in algebra, free objects are relatively easily understood objects and other algebraic structures can be systematically studied in terms of subquotients of free things.
chromotopy.org/?p=198
Plasmonic Silver Nanostructures for many sensings applications
]]> Email ThisBlogThis!Share to TwitterShare to Facebook TweetA*Star Research - Silver nanostructures exhibit a resonance feature that is useful for a multitude of sensing applications. A dual-disk ring (DDR) structure with broken symmetry and weakly dissipating material, silver, is proposed to achieve Fano resonance in visible wavelength range.
nextbigfuture.com/2012/06/plasmonic-silver-nanostructures-for.html
Proving there is only 1 GTO with 41 easy steps. : Poker Theory : Poker Forums at DeucesCracked.com
No sign-up fees, no DRM, and a FREE trial. Free strategy discussions, podcast, and articles. See what makes DeucesCracked different.
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Weak solution and Galerkin method of parabolic equation | lim Practice= Perfect
when time goes to infinity (by Sun's World)
sunlimingbit.wordpress.com/2013/04/02/weak-solution-and-galerkin-method-of-parabolic-equation/
harrydraco: Finite Incantatum - chaper 10
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Euler characteristic in nLab
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