Generalized Stable Rings and Regularity

2012 ◽  
Vol 19 (01) ◽  
pp. 159-168
Author(s):  
Huanyin Chen
Keyword(s):  
Stable Property ◽  
Diagonal Reduction ◽  
Regular Rings

We prove in this article that the generalized stable property is invariant under Morita contexts. Further, we show that many classes of square matrices over generalized stable regular rings admit a diagonal reduction. Related examples are constructed as well.

The Myth of Rigorous Accounting Research

2014 ◽  
Vol 28 (4) ◽  
pp. 869-887 ◽  
Author(s):  
Paul F. Williams
Keyword(s):  
Statistical Models ◽  
Policy Recommendations ◽  
Stable Property ◽  
Accounting Research

SYNOPSIS In this brief paper, I provide an argument that the rigor that allegedly characterizes contemporary mainstream accounting research is a myth. Expanding on arguments provided by West (2003), Gillies (2004), and Williams (1989), I show that the numbers utilized extensively to construct the statistical models that are the central defining feature of rigorous accounting research are, in many cases, not adequate to the task. These numbers are operational numbers that cannot be construed as measures or quantities of any kind of stable property. Constructing elaborate calculative models using operational numbers leads to equations whose results are not clearly decipherable. The rigorous nature of certain preferred forms of accounting research is, thus, largely a matter of appearance and not a substantive quality of the research mode that we habitually label “rigorous.” Thus, the policy recommendations implied by the results of rigorous accounting research may be viewed with considerable skepticism.

RATIONALLY ℵα-COMPLETE COMMUTATIVE RINGS OF QUOTIENTS

2009 ◽  
Vol 08 (05) ◽  
pp. 601-615
Author(s):  
JOHN D. LAGRANGE
Keyword(s):  
Commutative Rings ◽  
Von Neumann ◽  
Von Neumann Regular Rings ◽  
Von Neumann Regular ◽  
Ring Of Quotients ◽  
Rings Of Quotients ◽  
Special Case ◽  
Regular Rings

If {Ri}i ∈ I is a family of rings, then it is well-known that Q(Ri) = Q(Q(Ri)) and Q(∏i∈I Ri) = ∏i∈I Q(Ri), where Q(R) denotes the maximal ring of quotients of R. This paper contains an investigation of how these results generalize to the rings of quotients Qα(R) defined by ideals generated by dense subsets of cardinality less than ℵα. The special case of von Neumann regular rings is studied. Furthermore, a generalization of a theorem regarding orthogonal completions is established. Illustrative example are presented.

On (Strongly) Gorenstein Von Neumann Regular Rings

2011 ◽  
Vol 39 (9) ◽  
pp. 3242-3252 ◽  
Author(s):  
Najib Mahdou ◽  
Mohammed Tamekkante ◽  
Siamak Yassemi
Keyword(s):  
Von Neumann ◽  
Von Neumann Regular Rings ◽  
Von Neumann Regular ◽  
Regular Rings

On feckly polar rings

2019 ◽  
Vol 18 (02) ◽  
pp. 1950021
Author(s):  
Tugce Pekacar Calci ◽  
Huanyin Chen
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Structure Theorems ◽  
Regular Rings

In this paper, we introduce a new notion which lies properly between strong [Formula: see text]-regularity and pseudopolarity. A ring [Formula: see text] is feckly polar if for any [Formula: see text] there exists [Formula: see text] such that [Formula: see text] Many structure theorems are proved. Further, we investigate feck polarity for triangular matrix and matrix rings. The relations among strongly [Formula: see text]-regular rings, pseudopolar rings and feckly polar rings are also obtained.

Local-global results for regular rings

1976 ◽  
Vol 4 (9) ◽  
pp. 811-821 ◽  
Author(s):  
Freddy Van Oystaeyen ◽  
Jan Van Geel
Keyword(s):  
Regular Rings

Representations of regular rings o f finite index-II

1993 ◽  
Vol 21 (11) ◽  
pp. 4173-4177 ◽  
Author(s):  
Andrew B. Carson
Keyword(s):  
Finite Index ◽  
Regular Rings
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