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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Dedekind-finite ring
Nov 27, 2008 ... A ring is said to be Dedekind-finite if for , implies . Certainly if is .... Thus, a ring is weakly -finite if and only if it is Dedekind-finite. Note 1. Weakly ...
moonstone.math.ncku.edu.tw/mathwiki/pmfield.php?n=MathWiki.Dedekind-finiteRings
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On Weakly Finite Conductor Rings - ResearchGate
ABSTRACT We define a weakly finite conductor rings with zero divisors, and examine the transfer of these rings to the trivial ring extensions. These results ...
www.researchgate.net/publication/232944340_On_Weakly_Finite_Conductor_Rings
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On linear groups over weakly locally finite division rings
May 20, 2013 ... Mathematics > Rings and Algebras ... Abstract: In this paper, we give the definition of {\em weakly locally finite} division rings and we show that ...
arxiv.org/abs/1305.4423
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o^/^/r^/r —0, - American Mathematical Society
ON MAKING RINGS WEAKLY FINITE. PETER MALCOLMSON. Abstract. Given an associative ring R with unit we construct the largest homo- morphic image of R  ...
www.ams.org/proc/1980-080-02/S0002-9939-1980-0577746-5/S0002-9939-1980-0577746-5.pdf
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On Weakly Finite Conductor Rings
Jan 30, 2012 ... We define a weakly finite conductor rings with zero divisors, and examine the transfer of these rings to the trivial ring extensions. These results ...
www.tandfonline.com/doi/abs/10.1081/AGB-200028231
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On Weakly Finite Conductor Rings
We define a weakly finite conductor rings with zero divisors, and examine the transfer of these rings to the trivial ring extensions. These results provide exam-.
www.tandfonline.com/doi/pdf/10.1081/AGB-200028231
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1. Rings whose cyclics have finite Goldie dimension - the Ohio ...
ﬁnite Goldie dimension if and only if every direct sum of (weakly) injective right ... right Noetherian rings as those for which direct sums of injective right modules ...
www.math.ohiou.edu/~jain/034.pdf
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WEAKLY FINITE MATRIX LOCALIZATIONS R. P. M. Cohn has ...
A ring is called weakly finite if all of its right invertible square matrices are invertible. ... square matrices over a ring, there is the notion of the (universal) matrix ...
jlms.oxfordjournals.org/content/s2-48/1/31.full.pdf
Search results for "Weakly finite ring"
Weakly finite ring in science
[PDF]1. Rings whose cyclics have finite Goldie dimension - the Ohio ...
Department of Mathematics, Ohio University, Athens, Ohio 45 701 ... ﬁnite Goldie dimension if and only if every direct sum of (weakly) injective right ... right Noetherian rings as those for which direct sums of injective right modules are injective.
On linear groups over weakly locally finite division rings
May 20, 2013 ... Mathematics > Rings and Algebras ... Abstract: In this paper, we give the definition of {\em weakly locally finite} division rings and we show that ...
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 ...
On linear groups over weakly locally finite division rings ...
Publication » On linear groups over weakly locally finite division rings. ... Vestnik St Petersburg University Mathematics 01/2013; 46(1). Data provided are for ...
[PDF]Free Ideal Rings and Localization in General Rings - School of ...
Apr 1, 2011 ... Published in the United States of America by Cambridge University Press, New ...... As an example of Weakly finite rings we have projective-.
Weakly Special Classes of Semiprime Rings - Springer
The class of all finite subdirect products of uniformly strongly prime rings is shown ... School of Mathematics, Statistics and Information Technology, University of ...
Modules whose Injective Endomorphisms Are Essential
Some other properties of weakly co-Hopfian modules are also obtained. The ring R is said to be right strong stably finite if all the finitely generated free right ...
Theory of Rings and Modules Abstracts - The Ohio State University
-module is of finite length over its endomorphism ring. ..... Characterizations of rings over which every weakly injective is weakly projective and conversely are ...
[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 ...
[PDF]WEAKLY DUO RINGS WITH NIL JACOBSON RADICAL Hong Kee ...
that one-sided Artinian rings and locally finite rings are strongly π-regular. ... third named author was supported by Pusan National University Research Grant.
Books on the term Weakly finite ring
Ring Theory, 83: Student Edition
Louis H. Rowen, 2012
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
Paul M. Cohn, 2003
... AB = I, BA = I, then m—n. (ii) For any ring R, the following conditions are equivalent: (a) R is weakly finite; (b) for anyn,R"^H®R"=>H = 0; (c) for any n, if A, B e R„ and AB — I, then BA — I. Moreover, any non-trivial Weakly finite ring has IBN ...
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
P. M. Cohn, 2006
Leti? be a weakly w-finite ring. Given maps a : Rr — > R" and/6 : R" — > Rs(r + s = n) such that afi = 0, a has a right inverse and p has a left inverse, then there exists an automorphism \x of R" such that a/j. : R' -> /?" is the natural inclusion and ...
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
that the ring Rp = S−1R is local with radRp = pRp, the ideal generated by the canonical image of p in Rp. (ii) Prove that ... (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 ...
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
Flat finite type ring extensions | Stacks Project Blog
Posted on August 20, 2010 by Johan.
math.columbia.edu/~dejong/wordpress/?p=753
Von Neumann Regular Rings Satisfying Weak Comparability | Applied Categorical Structures - Official Blog
by Kutami, Mamoru The notion of weak comparability was first introduced by K.C. O’Meara, to prove that directly finite simple regular rings satisfying weak
blogs.springer.com/apcs/articles/von-neumann-regular-rings-satisfying-weak-comparability/
Benjamin’s notes » Blog Archive » Finite Rings With Identity (Pure & Applied Mathematics) download ebook
Finite Rings With Identity (Pure & Applied Mathematics) by Bernard R. McDonald Download Finite Rings With Identity (Pure & Applied Mathematics) Finite Rings With Identity (Pure & Applied Mathematics) Bernard R.