Perfect ring-like beam

2012 ◽  
Vol 6 (4) ◽  
pp. 217-219 ◽  
Author(s):  
Andrei A. Fotiadi ◽  
Patrice Mégret
Keyword(s):  
Perfect Ring

WHEN SELF-INJECTIVE RINGS ARE QF: A REPORT ON A PROBLEM

2002 ◽  
Vol 01 (01) ◽  
pp. 75-105 ◽  
Author(s):  
CARL FAITH ◽  
DINH VAN HUYNH
Keyword(s):  
Perfect Ring ◽  
Survey Results ◽  
Cs Rings

Theorems of Osofsky and Kato imply that a right and left self-injective one-sided perfect ring is quasi-Frobenius (= QF). The corresponding question for one-sided self-injective one or two-sided perfect rings remains open, even assuming that the ring is semiprimary. The latter version of the problem is known as Faith's Conjecture (FC). We survey results on QF rings, especially those obtained in connection with FC. We also review various results that provide partial answers to another problem of Faith: Is a right FGF ring necessarily QF? On this topic, we provide a new result, namely that if all factor rings of R are right FGF, then R is QF (Theorem 6.1). In Sec. 7 we review results concerning the question of when a D-ring is QF. Sections 8 and 9 are devoted respectively to IF rings, and to Σ-injective rings and Σ-CS rings.

A conception of zero-divisor graph for categories of modules

2015 ◽  
Vol 15 (01) ◽  
pp. 1650012
Author(s):  
Afshin Amini ◽  
Babak Amini ◽  
Ehsan Momtahan
Keyword(s):  
Zero Divisor ◽  
Chromatic Numbers ◽  
Perfect Ring ◽  
Zero Divisor Graph

We introduce and study zero-divisor graphs in categories of left modules over a ring R, i.e. R- MOD . The vertices of Γ(R- MOD ) consist of all nonzero morphisms in R- MOD which are not isomorphisms. Two vertices f and g are adjacent if f ◦ g = 0 or g ◦ f = 0. We observe that these graphs are connected and their diameter is equal or less than four. We prove that Γ(R- MOD ) = 3 if and only if R is a right and left perfect ring and R/J(R) is simple artinian. We also characterize all vertices with complements and that when a kernel or a co-kernel can be a complement for a morphism. Some discussions will be made on radius of these graphs, their clique and chromatic numbers.

Generation and Manipulation of Multiple Magnetic Fano Resonances in Split Ring-Perfect Ring Nanostructure

Plasmonics ◽  
2016 ◽  
Vol 12 (5) ◽  
pp. 1613-1619 ◽  
Author(s):  
Yuan Li ◽  
Yiping Huo ◽  
Ying Zhang ◽  
Zhongyue Zhang
Keyword(s):  
Fano Resonances ◽  
Split Ring ◽  
Perfect Ring

scholarly journals The skeleton of a perfect ring

1971 ◽  
Vol 17 (4) ◽  
pp. 451-459 ◽  
Author(s):  
Garry Helzer
Keyword(s):  
Perfect Ring

scholarly journals Cotorsion radicals and projective modules

1971 ◽  
Vol 5 (2) ◽  
pp. 241-253 ◽  
Author(s):  
John A. Beachy
Keyword(s):  
Projective Module ◽  
Projective Modules ◽  
Left Module ◽  
Perfect Ring ◽  
Artinian Rings ◽  
Trace Ideal ◽  
Dual Notion ◽  
Rings Of Quotients ◽  
Torsion Radical ◽  
Natural Way

We study the notion (for categories of modules) dual to that of torsion radical and its connections with projective modules.Torsion radicals in categories of modules have been studied extensively in connection with quotient categories and rings of quotients. (See [8], [12] and [13].) In this paper we consider the dual notion, which we have called a cotorsion radical. We show that the cotorsion radicals of the category RM correspond to the idempotent ideals of R. Thus they also correspond to TTF classes in the sense of Jans [9].It is well-known that the trace ideal of a projective module is idempotent. We show that this is in fact a consequence of the natural way in which every projective module determines a cotorsion radical. As an application of these techniques we study a question raised by Endo [7], to characterize rings with the property that every finitely generated, projective and faithful left module is completely faithful. We prove that for a left perfect ring this is equivalent to being an S-ring in the sense of Kasch. This extends the similar result of Morita [15] for artinian rings.

A note on dual automorphism invariant modules

2017 ◽  
Vol 16 (02) ◽  
pp. 1750024
Author(s):  
C. Selvaraj ◽  
S. Santhakumar
Keyword(s):  
Projective Module ◽  
Exchange Property ◽  
Sufficient Condition ◽  
Cyclic Module ◽  
Necessary And Sufficient Condition ◽  
Perfect Ring ◽  
Necessary And Sufficient

In this paper, we investigate some properties of dual automorphism invariant modules over right perfect rings. Also, we introduce the notion of dual automorphism invariant cover and prove the existence of dual automorphism invariant cover. Moreover, we give the necessary and sufficient condition for every cyclic module to be a dual automorphism invariant module over a semi perfect ring and we prove that supplemented quasi projective module has finite exchange property. Also we give a characterization of a perfect ring using dual automorphism invariant module.

scholarly journals Hoag's object: the quintessential ring galaxy

2012 ◽  
Vol 10 (H16) ◽  
pp. 368-368
Author(s):  
Noah Brosch ◽  
Ido Finkelman ◽  
Alexei Moiseev
Keyword(s):  
Star Formation ◽  
Elliptical Galaxy ◽  
Neutral Hydrogen ◽  
Perfect Ring ◽  
Large Disk ◽  
Low Level ◽  
The Core ◽  
Event Triggered

AbstractWe present new observations of Hoag's Object, known as “the most perfect ring galaxy,“ that show that a preferred explanation for this object is (a) the formation of a triaxial elliptical galaxy some 10 Gyr ago, (b) the accretion of a large disk of neutral hydrogen at about the same time, (c) low-level star formation in the HI disk for all the time since that event triggered by the triaxial potential of the core.

scholarly journals A noncommutative generalization of Auslander's last theorem

2005 ◽  
Vol 2005 (9) ◽  
pp. 1473-1480
Author(s):  
Edgar E. Enochs ◽  
Overtoun M. G. Jenda ◽  
J. A. López-Ramos
Keyword(s):  
Projective Cover ◽  
Finitely Generated ◽  
Perfect Ring ◽  
Dualizing Module ◽  
Auslander Class

We show that every finitely generated leftR-module in the Auslander class over ann-perfect ringRhaving a dualizing module and admitting a Matlis dualizing module has a Gorenstein projective cover.

scholarly journals On quasi-duo rings

1995 ◽  
Vol 37 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Hua-Ping Yu
Keyword(s):  
Natural Number ◽  
Left Ideal ◽  
Commutative Rings ◽  
Noncommutative Rings ◽  
Perfect Ring ◽  
Maximal Submodule ◽  
Bass Conjecture ◽  
Infinite Sets

Bass [1] proved that if R is a left perfect ring, then R contains no infinite sets of orthogonal idempotents and every nonzero left R-module has a maximal submodule, and asked if this property characterizes left perfect rings ([1], Remark (ii), p. 470). The fact that this is true for commutative rings was proved by Hamsher [12], and that this is not true in general was demonstrated by examples of Cozzens [7] and Koifman [14]. Hamsher's result for commutative rings has been extended to some noncommutative rings. Call a ring left duo if every left ideal is two-sided; Chandran [5] proved that Bass’ conjecture is true for left duo rings. Call a ring R weakly left duo if for every r ε R, there exists a natural number n(r) (depending on r) such that the principal left ideal Rrn(r) is two-sided. Recently, Xue [21] proved that Bass’ conjecture is still true for weakly left duo rings.

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