A Note on Quasi-Frobenius Rings and Ring Epimorphisms

1969 ◽  
Vol 12 (3) ◽  
pp. 287-292 ◽  
Author(s):  
H. H. Storrer
Keyword(s):  
Unit Element ◽  
Usual Condition ◽  
Annihilator Ideal ◽  
Frobenius Rings ◽  
Weakened Form

In this note, we characterize quasi-Frobenius rings by a weakened form of the usual condition, that every ideal is an annihilator ideal.We then apply this result to pure rings in the sense of Cohn and to dominant rings, a concept arising in the study of ring epimorphisms. All rings considered have a unit element.

scholarly journals The diameter of annihilator ideal graph of ℤn

2021 ◽  
Author(s):  
Ami Rahmawati ◽  
Vika Yugi Kurniawan ◽  
Supriyadi Wibowo
Keyword(s):  
Annihilator Ideal

scholarly journals Wideband Circular Polarized Dielectric Resonator Antenna Array for Millimeter-Wave Applications

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3614
Author(s):  
Arun Kesavan ◽  
Mu’ath Al-Hassan ◽  
Ismail Ben Mabrouk ◽  
Tayeb A. Denidni
Keyword(s):  
Antenna Array ◽  
Millimeter Wave ◽  
Axial Ratio ◽  
Unit Element ◽  
Dielectric Resonator Antenna ◽  
Gain Bandwidth ◽  
Left Hand ◽  
Wide Resonance ◽  
Element Array ◽  
Peak Gain

A novel circular polarized dielectric antenna array (DRA) for millimeter-wave applications at 30 GHz is presented in this paper. The unit element array is a flower-shaped DRA fed with a cross slot. To obtain circular polarization, a sequential network combined with the cross slots is used to feed the 2×2 array. The prototype of the proposed antenna array is fabricated and measured to obtain a wide resonance bandwidth from 27 GHz to 38 GHz frequency band. Furthermore, this left-hand polarized antenna array has achieved a peak gain of 9.5 dBi with 3-dB axial ratio at 30 GHz. The proposed DRA array with wideband resonance and gain bandwidth has the potential to be used for millimeter-wave wireless communications at the 30 GHz band.

scholarly journals C-Band and X-Band Switchable Frequency-Selective Surface

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 476
Author(s):  
Umer Farooq ◽  
Adnan Iftikhar ◽  
Muhammad Farhan Shafique ◽  
Muhammad Saeed Khan ◽  
Adnan Fida ◽  
...  
Keyword(s):  
Bottom Layer ◽  
Frequency Selective Surface ◽  
Transverse Magnetic ◽  
Unit Element ◽  
Angular Stability ◽  
Band Spectrum ◽  
Pin Diode ◽  
Pin Diodes ◽  
X Band ◽  
Frequency Selective

This paper presents a highly compact frequency-selective surface (FSS) that has the potential to switch between the X-band (8 GHz–12 GHz) and C-band (4 GHz–8 GHz) for RF shielding applications. The proposed FSS is composed of a square conducting loop with inward-extended arms loaded with curved extensions. The symmetric geometry allows the RF shield to perform equally for transverse electric (TE), transverse magnetic (TM), and 45° polarizations. The unit cell has a dimension of 0.176 λ0 and has excellent angular stability up to 60°. The resonance mechanism was investigated using equivalent circuit models of the shield. The design of the unit element allowed incorporation of PIN diodes between adjacent elements for switching to a lower C-band spectrum at 6.6 GHz. The biasing network is on the bottom layer of the substrate to avoid effects on the shielding performance. A PIN diode configuration for the switching operation was also proposed. In simulations, the PIN diode model was incorporated to observe the switchable operation. Two prototypes were fabricated, and the switchable operation was demonstrated by etching copper strips on one fabricated prototype between adjacent unit cells (in lieu of PIN diodes) as a proof of the design prototypes. Comparisons among the results confirmed that the design offers high angular stability and excellent performance in both bands.

scholarly journals New bounds for codes over finite Frobenius rings

2010 ◽  
Vol 57 (2) ◽  
pp. 169-179 ◽  
Author(s):  
Eimear Byrne ◽  
Marcus Greferath ◽  
Axel Kohnert ◽  
Vitaly Skachek
Keyword(s):  
Frobenius Rings ◽  
Finite Frobenius Rings

Completely Indecomposable Modules

1949 ◽  
Vol 1 (2) ◽  
pp. 125-152 ◽  
Author(s):  
Ernst Snapper
Keyword(s):  
Abelian Group ◽  
Commutative Ring ◽  
Chain Condition ◽  
Indecomposable Module ◽  
Unit Element ◽  
Indecomposable Modules ◽  
Operator Domain ◽  
Unit Operator ◽  
Ascending Chain Condition

The purpose of this paper is to investigate completely indecomposable modules. A completely indecomposable module is an additive abelian group with a ring A as operator domain, where the following four conditions are satisfied.1-1. A is a commutative ring and has a unit element which is unit operator for .1-2. The submodules of satisfy the ascending chain condition. (Submodule will always mean invariant submodule.)

On the Valuation of Industrial Assurance Policies

1912 ◽  
Vol 1 (02) ◽  
pp. 31-38
Author(s):  
R. C. Fippard
Keyword(s):  
Medical Examination ◽  
Usual Condition ◽  
Special Cases ◽  
Second Period

The general principles on which a valuation should be made are the same for Industrial as for Ordinary Assurance policies, but the differences between the two classes of business necessitate considerable difference in the methods by which these principles are applied.The greater number of Industrial Assurance policies are issued on the basis of the weekly payment of id. and small multiples of id., the premiums being collected weekly by agents. The average sum assured is consequently small and the expense of collection relatively great. Medical examination is not asked for except in special cases, the agents being required to form their own opinion of the eligibility for insurance of the proposer. The effects of serious errors of judgment in this matter are minimised by the usual condition that a proportion only—usually one quarter—of the sum assured shall be paid should death occur otherwise than by accident during the first three or six months of the assurance; the proportion being increased to one-half for the second period of three or six months; and the full sum assured being payable thereafter.

scholarly journals Another single law for groups

1981 ◽  
Vol 23 (1) ◽  
pp. 81-102 ◽  
Author(s):  
B.H. Neumann
Keyword(s):  
Unit Element ◽  
Minimal Length ◽  
And Inversion

It has long been known that, in terms of right division, groups can be defined by a single law. In this paper a single law defining groups in terms of multiplication and inversion is proposed. This law is in 4 variables, and it is conjectured that no fewer than 4 variables will do, and that the proposed law is of minimal length as well. Some extensions of the result, and an alternative single law with the same length and number of variables, are also discussed. By contrast, groups in terms of multiplication, inversion, and a unit element can not be defined by a single law. Most of these results were stated by Tarski at the Logic Colloquium at Hannover in 1966, but apparently no proof has yet been published.

The existence of a positive solution to asymptotically linear scalar field equations

2000 ◽  
Vol 130 (1) ◽  
pp. 81-105 ◽  
Author(s):  
G. Li ◽  
H.-S. Zhou
Keyword(s):  
Positive Solution ◽  
Nonlinear Term ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Field Equations ◽  
Usual Condition ◽  
Image Position ◽  
Scalar Field Equations ◽  
Constraint Method ◽  
Linear Scalar

We consider the following elliptic equation: where m > 0, f(x, u)/u tends to a positive constant as u → + ∞. Here, the nonlinear term f(x, u) does not satisfy the usual condition, that is, for some θ > 0, which is important in using the mountain pass theorem. The aim of this paper is to discuss how to use the mountain pass theorem to show the existence of a positive solution to the present problem when we lose the above condition. Furthermore, if f(x, u) ≡ f(u), we also prove that the above problem has a ground state by using the artificial constraint method.

scholarly journals On the Structure of Graded Leibniz Algebras

2015 ◽  
Vol 22 (01) ◽  
pp. 83-96 ◽  
Author(s):  
Antonio J. Calderón Martín ◽  
José M. Sánchez Delgado
Keyword(s):  
Arbitrary Dimension ◽  
Unit Element ◽  
Homogeneous Component ◽  
Maximal Length ◽  
Base Field ◽  
Leibniz Algebras ◽  
Arbitrary Base

We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field 𝕂. We show that any of such algebras 𝔏 with a symmetric G-support is of the form [Formula: see text] with U a subspace of 𝔏1, the homogeneous component associated to the unit element 1 in G, and any Ij a well described graded ideal of 𝔏, satisfying [Ij, Ik]=0 if j ≠ k. In the case of 𝔏 being of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.

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