The Ring and Exchange-Ring Approximations Based on Kohn–Sham Reference States

2014 ◽  
pp. 97-144 ◽  
Author(s):  
Andreas Heßelmann
Keyword(s):  
Exchange Ring

A novel bartering exchange ring based incentive mechanism for peer-to-peer systems

2013 ◽  
Vol 29 (1) ◽  
pp. 361-369 ◽  
Author(s):  
Kan Zhang ◽  
Nick Antonopoulos
Keyword(s):  
Incentive Mechanism ◽  
Peer To Peer ◽  
Exchange Ring ◽  
Peer To Peer Systems

EXCHANGE RINGS OVER WHICH EVERY REGULAR MATRIX ADMITS DIAGONAL REDUCTION

2004 ◽  
Vol 03 (02) ◽  
pp. 207-217 ◽  
Author(s):  
HUANYIN CHEN
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Exchange Ring ◽  
Regular Matrix ◽  
Finitely Generated ◽  
Exchange Rings ◽  
Necessary And Sufficient ◽  
Diagonal Reduction

In this paper, we investigate the necessary and sufficient conditions on exchange rings, under which every regular matrix admits diagonal reduction. Also we show that an exchange ring R is strongly separative if and only if for any finitely generated projective right R-module C, if A and B are any right R-modules such that 2C⊕A≅C⊕B, then C⊕A≅B.

On Exchange Hermitian Rings

2010 ◽  
Vol 17 (01) ◽  
pp. 87-100 ◽  
Author(s):  
Huanyin Chen
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Exchange Ring ◽  
Regular Matrix ◽  
Exchange Rings ◽  
Necessary And Sufficient ◽  
Diagonal Reduction

In this article, we investigate new necessary and sufficient conditions on an exchange ring under which every regular matrix admits a diagonal reduction. We prove that an exchange ring R is an hermitian ring if and only if for any n ≥ 2 and any regular x ∈ Rn, there exists u ∈ CLn(R) such that x = xux; if and only if for any n ≥ 2 and any regular x ∈ Rn, there exists u ∈ CLn(R) such that xu ∈ R is an idempotent. Furthermore, we characterize such exchange rings by means of reflexive inverses and n-pseudo-similarity.

scholarly journals Exchange rings having stable range one

2001 ◽  
Vol 25 (12) ◽  
pp. 763-770 ◽  
Author(s):  
Huanyin Chen
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Stable Range ◽  
Exchange Ring ◽  
Stable Range One ◽  
Exchange Rings

We investigate the sufficient conditions and the necessary conditions on an exchange ringRunder whichRhas stable range one. These give nontrivial generalizations of Theorem 3 of V. P. Camillo and H.-P. Yu (1995), Theorem 4.19 of K. R. Goodearl (1979, 1991), Theorem 2 of R. E. Hartwig (1982), and Theorem 9 of H.-P. Yu (1995).

scholarly journals Elements in exchange rings with related comparability

2000 ◽  
Vol 23 (9) ◽  
pp. 639-644 ◽  
Author(s):  
Huanyin Chen
Keyword(s):  
Exchange Ring ◽  
Dual Problems ◽  
Exchange Rings ◽  
Related Comparability

We show that ifRis an exchange ring, then the following are equivalent: (1)Rsatisfies related comparability. (2) Givena,b,d∈RwithaR+bR=dR, there exists a related unitw∈Rsuch thata+bt=dw. (3) Givena,b∈RwithaR=bR, there exists a related unitw∈Rsuch thata=bw. Moreover, we investigate the dual problems for rings which are quasi-injective as right modules.

scholarly journals A CLASS OF EXCHANGE RINGS

2008 ◽  
Vol 50 (3) ◽  
pp. 509-522 ◽  
Author(s):  
TSIU-KWEN LEE ◽  
YIQIANG ZHOU
Keyword(s):  
Exchange Ring ◽  
Glasgow Math ◽  
Basic Properties ◽  
Boolean Rings ◽  
Clean Rings ◽  
Exchange Rings

AbstractIt is well known that a ring R is an exchange ring iff, for any a ∈ R, a−e ∈ (a2−a)R for some e2 = e ∈ R iff, for any a ∈ R, a−e ∈ R(a2−a) for some e2 = e ∈ R. The paper is devoted to a study of the rings R satisfying the condition that for each a ∈ R, a−e ∈ (a2−a)R for a unique e2 = e ∈ R. This condition is not left–right symmetric. The uniquely clean rings discussed in (W. K. Nicholson and Y. Zhou, Rings in which elements are uniquely the sum of an idempotent and a unit, Glasgow Math. J. 46 (2004), 227–236) satisfy this condition. These rings are characterized as the semi-boolean rings with a restricted commutativity for idempotents, where a ring R is semi-boolean iff R/J(R) is boolean and idempotents lift modulo J(R) (or equivalently, R is an exchange ring for which any non-zero idempotent is not the sum of two units). Various basic properties of these rings are developed, and a number of illustrative examples are given.

Endomorphisms of Progenerators over Exchange QB-Rings

2008 ◽  
Vol 15 (03) ◽  
pp. 493-500
Author(s):  
Huanyin Chen
Keyword(s):  
Exchange Ring

In this paper, we characterize exchange QB-rings by endomorphisms of progenerators. Let A be a progenerator over an exchange ring R. It is shown that R is a QB-ring if and only if whenever f, g, h ∈ End RA satisfy fA + gA = hA, there exist [Formula: see text] and l ∈ End RA such that fk + gl = h. Some applications are also obtained.

scholarly journals ON PSEUDO SEMISIMPLE RINGS

2012 ◽  
Vol 12 (02) ◽  
pp. 1250162
Author(s):  
ENGİN BÜYÜKAŞIK ◽  
SAAD H. MOHAMED ◽  
HATİCE MUTLU
Keyword(s):  
Sufficient Condition ◽  
Exchange Ring ◽  
Necessary And Sufficient Condition ◽  
Semisimple Ring ◽  
Necessary And Sufficient

A necessary and sufficient condition is obtained for a right pseudo semisimple ring to be left pseudo semisimple. It is proved that a right pseudo semisimple ring is an internal exchange ring. It is also proved that a right and left pseudo semisimple ring is an SSP ring.

scholarly journals Duo property for rings by the quasinilpotent perspective

2021 ◽  
Vol 13 (2) ◽  
pp. 485-500
Author(s):  
A. Harmanci ◽  
Y. Kurtulmaz ◽  
B. Ungor
Keyword(s):  
Stable Range ◽  
Exchange Ring ◽  
Series Ring

In this paper, we focus on the duo ring property via quasinilpotent elements, which gives a new kind of generalizations of commutativity. We call this kind of rings qnil-duo. Firstly, some properties of quasinilpotents in a ring are provided. Then the set of quasinilpotents is applied to the duo property of rings, in this perspective, we introduce and study right (resp., left) qnil-duo rings. We show that this concept is not left-right symmetric. Among others, it is proved that if the Hurwitz series ring $H(R; \alpha)$ is right qnil-duo, then $R$ is right qnil-duo. Every right qnil-duo ring is abelian. A right qnil-duo exchange ring has stable range 1.

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