scholarly journals On nilpotency of the right singular ideal of semiring

2017 ◽  
Vol 37 (2) ◽  
pp. 123-127
Author(s):  
Nabanita Goswami ◽  
Helen K. Saikia
Keyword(s):  
Singular Ideal ◽  
The Right

We introduce the concept of nilpotency of the right singular ideal of a semiring. We discuss some properties of such nilpotency and singular ideals. We show that the right singular ideal of a semiring with a.c.c. for right annihilators, is nilpotent.

On Ring Properties of Injective Hulls

1975 ◽  
Vol 18 (2) ◽  
pp. 233-239 ◽  
Author(s):  
N. C. Lang
Keyword(s):  
Regular Ring ◽  
Associative Ring ◽  
Injective Hull ◽  
Von Neumann ◽  
Singular Ideal ◽  
The Right ◽  
Injective Hulls

Let R be an associative ring and denote by the injective hull of the right module RR. If can be endowed with a ring multiplication which extends the existing module multiplication, we say that is a ring and the statement that R is a ring will always mean in this sense.It is known that is a regular ring (in the sense of von Neumann) if and only if the singular ideal of R is zero.

Study of Semi-projective Retractable Modules

2007 ◽  
Vol 14 (03) ◽  
pp. 489-496 ◽  
Author(s):  
A. Haghany ◽  
M. R. Vedadi
Keyword(s):  
Endomorphism Ring ◽  
Semiprime Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Singular Ideal ◽  
The Right ◽  
Necessary And Sufficient

For a semi-projective retractable module MR with endomorphism ring S, we prove u.dim MR= u.dim SS, and find necessary and sufficient conditions on M in order that S be respectively semiprime, right nonsingular, finitely cogenerated, cocyclic, or weakly co-Hopfian. Precise descriptions of the right singular ideal of S and the socle of M are given, and in addition if S is a semiprime ring, it is shown that MR is FI-extending if and only if SS is FI-extending.

The set of singular elements of a ring with respect to a module

2018 ◽  
Vol 13 (03) ◽  
pp. 2050050
Author(s):  
A. Farzi–Safarabadi ◽  
R. Beyranvand
Keyword(s):  
Matrix Ring ◽  
Triangular Matrix ◽  
Semisimple Module ◽  
Prime Module ◽  
Triangular Matrix Ring ◽  
Singular Ideal ◽  
The Right

Let [Formula: see text] be a ring and [Formula: see text] be a right [Formula: see text]-module. In this paper, we introduce the set [Formula: see text] for some essential submodule [Formula: see text] of [Formula: see text] of singular elements of[Formula: see text] with respect to[Formula: see text] , and we investigate the properties of it. For example, it is shown that [Formula: see text] is an ideal of [Formula: see text] and [Formula: see text]. Also if [Formula: see text] is a semiprime right Goldie ring, then [Formula: see text], where [Formula: see text] is the right singular ideal of [Formula: see text]. We prove that if [Formula: see text] is a semisimple module or a prime module, then [Formula: see text]. For any submodule [Formula: see text] of [Formula: see text], we have [Formula: see text] and if [Formula: see text], then [Formula: see text]. We show that [Formula: see text] and [Formula: see text]. In the end, the singular elements of some rings with respect to the formal triangular matrix ring are investigated.

scholarly journals Structure of pseudo-semisimple rings

1991 ◽  
Vol 50 (1) ◽  
pp. 53-66 ◽  
Author(s):  
Saad Mohamed ◽  
Bruno J. Müller
Keyword(s):  
Structure Theorem ◽  
Complete Characterization ◽  
Infinite Dimensional ◽  
Singular Ideal ◽  
The Right

AbstractA ring R is called right pseudo-semisimple if every right ideal not isomorphic to R is semisimpie. Rings of this type in which the right socle S splits off additively were characterized; such a ring has S2 = 0. The existence of right pseudo-semisimple rings with zero right singular ideal Z remained open, except for the trivial examples of semisimple rings and principal right ideal domains. In this work we give a complete characterization of right pseudo-semisimple rings with S2 = 0. We also give examples of non-trivial right pseudo-semisimple rings with Z = 0; in fact it is shown that such rings exist as subrings in every infinite-dimensional full linear ring. A structure theorem for non-singular right pseudo-semisimple rings, with homogeneous maximal socle, is given. The general case is still open.

A Generalization of Semiregular and Almost Principally Injective Rings

2010 ◽  
Vol 17 (spec01) ◽  
pp. 905-916
Author(s):  
A. Çiğdem Özcan ◽  
Pınar Aydoğdu
Keyword(s):  
Jacobson Radical ◽  
Left And Right ◽  
Singular Ideal ◽  
The Right ◽  
The Ideal

In this article, we call a ring R right almost I-semiregular for an ideal I of R if for any a ∈ R, there exists a left R-module decomposition lRrR(a) = P ⊕ Q such that P ⊆ Ra and Q ∩ Ra ⊆ I, where l and r are the left and right annihilators, respectively. This generalizes the right almost principally injective rings defined by Page and Zhou, I-semiregular rings defined by Nicholson and Yousif, and right generalized semiregular rings defined by Xiao and Tong. We prove that R is I-semiregular if and only if for any a ∈ R, there exists a decomposition lRrR(a) = P ⊕ Q, where P = Re ⊆ Ra for some e2 = e ∈ R and Q ∩ Ra ⊆ I. Among the results for right almost I-semiregular rings, we show that if I is the left socle Soc (RR) or the right singular ideal Z(RR) or the ideal Z(RR) ∩ δ(RR), where δ(RR) is the intersection of essential maximal left ideals of R, then R being right almost I-semiregular implies that R is right almost J-semiregular for the Jacobson radical J of R. We show that δl(eRe) = e δ(RR)e for any idempotent e of R satisfying ReR = R and, for such an idempotent, R being right almost δ(RR)-semiregular implies that eRe is right almost δl(eRe)-semiregular.

Investor-State Dispute Settlement under NAFTA Chapter 11: The Shape of Things to Come?

1998 ◽  
Vol 35 ◽  
pp. 263-290
Author(s):  
J. Anthony VanDuzer
Keyword(s):  
Free Trade Agreement ◽  
Dispute Settlement ◽  
Trade Agreement ◽  
Minimum Standards ◽  
The North ◽  
State Behaviour ◽  
Nafta Chapter 11 ◽  
To Come ◽  
The Right

SummaryRecently, there has been a proliferation of international agreements imposing minimum standards on states in respect of their treatment of foreign investors and allowing investors to initiate dispute settlement proceedings where a state violates these standards. Of greatest significance to Canada is Chapter 11 of the North American Free Trade Agreement, which provides both standards for state behaviour and the right to initiate binding arbitration. Since 1996, four cases have been brought under Chapter 11. This note describes the Chapter 11 process and suggests some of the issues that may arise as it is increasingly resorted to by investors.

What face familiarity feelings say about the lateralization of specific entities within the core system

2019 ◽  
Vol 42 ◽  
Author(s):  
Guido Gainotti
Keyword(s):  
Temporal Lobe ◽  
Memory System ◽  
Core System ◽  
The Core ◽  
Memory Traces ◽  
Specific Memory ◽  
Target Article ◽  
Temporal Structures ◽  
The Right

Abstract The target article carefully describes the memory system, centered on the temporal lobe that builds specific memory traces. It does not, however, mention the laterality effects that exist within this system. This commentary briefly surveys evidence showing that clear asymmetries exist within the temporal lobe structures subserving the core system and that the right temporal structures mainly underpin face familiarity feelings.

Study of charge transfer in FeTi

1983 ◽  
Vol 41 ◽  
pp. 296-297
Author(s):  
J. Taft∅
Keyword(s):  
Charge Transfer ◽  
Charge Distribution ◽  
Electron Scattering ◽  
Periodic System ◽  
Electron Distribution ◽  
Scattering Amplitude ◽  
Transition Elements ◽  
Hartree Fock ◽  
Cscl Structure ◽  
The Right

It is well known that for reflections corresponding to large interplanar spacings (i.e., sin θ/λ small), the electron scattering amplitude, f, is sensitive to the ionicity and to the charge distribution around the atoms. We have used this in order to obtain information about the charge distribution in FeTi, which is a candidate for storage of hydrogen. Our goal is to study the changes in electron distribution in the presence of hydrogen, and also the ionicity of hydrogen in metals, but so far our study has been limited to pure FeTi. FeTi has the CsCl structure and thus Fe and Ti scatter with a phase difference of π into the 100-ref lections. Because Fe (Z = 26) is higher in the periodic system than Ti (Z = 22), an immediate “guess” would be that Fe has a larger scattering amplitude than Ti. However, relativistic Hartree-Fock calculations show that the opposite is the case for the 100-reflection. An explanation for this may be sought in the stronger localization of the d-electrons of the first row transition elements when moving to the right in the periodic table. The tabulated difference between fTi (100) and ffe (100) is small, however, and based on the values of the scattering amplitude for isolated atoms, the kinematical intensity of the 100-reflection is only 5.10-4 of the intensity of the 200-reflection.

New Dimensions in Freeze-Etching

1969 ◽  
Vol 27 ◽  
pp. 202-203 ◽  
Author(s):  
Russell L. Steere ◽  
Michael Moseley
Keyword(s):  
Fracture Surfaces ◽  
Aluminum Specimen ◽  
Specimen Holder ◽  
Freeze Etching ◽  
The Right

A redesigned specimen holder and cap have made possible the freeze-etching of both fracture surfaces of a frozen fractured specimen. In principal, the procedure involves freezing a specimen between two specimen holders (as shown in A, Fig. 1, and the left side of Fig. 2). The aluminum specimen holders and brass cap are constructed so that the upper specimen holder can be forced loose, turned over, and pressed down firmly against the specimen stage to a position represented by B, Fig. 1, and the right side of Fig. 2.

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