Weakly finite ring
In algebra, a ring 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]

This is an excerpt from the article Weakly finite ring from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
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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
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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 ...
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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
Search results for "Weakly finite ring"
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
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 ...
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 ...
Ring Theory, Student Edition
1991
This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**"As a textbook for graduate students, Ring Theory joins the best....The e...
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
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'.
Free Ideal Rings and Localization in General Rings (New Mathematical Monographs)
2006
Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove t...
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 ...
Basic Algebra
2004
This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definit...

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Weakly finite ring
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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.
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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.
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