The complete matrix ring over an adjoint regular ring is adjoint regular

2009 ◽  
Vol 80 (1) ◽  
pp. 79-84
Author(s):  
Olga Finogenova
Keyword(s):  
Regular Ring ◽  
Matrix Ring ◽  
Complete Matrix

On 2-nil-good rings

2018 ◽  
Vol 17 (06) ◽  
pp. 1850110
Author(s):  
Marjan Sheibani Abdolyousefi ◽  
Nahid Ashrafi ◽  
Huanyin Chen
Keyword(s):  
Regular Ring ◽  
Matrix Ring ◽  
Good Property ◽  
Fundamental Properties ◽  
Lower Triangular ◽  
Square Matrix

A ring [Formula: see text] is defined to be 2-nil-good if every element in [Formula: see text] is the sum of two units and a nilpotent. Fundamental properties of such rings are obtained. We prove that every strongly [Formula: see text]-regular ring is 2-nil-good if and only if the identity is the sum of two units. One of the main result of this paper is that every square matrix ring over J-fine rings is 2-nil-good. We establish 2-nil-good property for Morita contexts. This implies, in particular, that every matrix ring over 2-nil-good rings is 2-nil-good. Furthermore, we prove that the ring [Formula: see text] of all lower triangular diagonal-finite matrices over a 2-good ring [Formula: see text] is 2-nil-good.

Rings whose cyclics are C3-modules

2016 ◽  
Vol 15 (08) ◽  
pp. 1650152 ◽  
Author(s):  
Yasser Ibrahim ◽  
Xuan Hau Nguyen ◽  
Mohamed F. Yousif ◽  
Yiqiang Zhou
Keyword(s):  
Direct Product ◽  
Regular Ring ◽  
Matrix Ring ◽  
Artinian Ring ◽  
Local Rings ◽  
Classical Theorem ◽  
Basic Properties ◽  
Semiperfect Ring ◽  
Injectivity Condition ◽  
Strongly Regular

It is well known that if every cyclic right module over a ring is injective, then the ring is semisimple artinian. This classical theorem of Osofsky promoted a considerable interest in the rings whose cyclics satisfy a certain generalized injectivity condition, such as being quasi-injective, continuous, quasi-continuous, or [Formula: see text]. Here we carry out a study of the rings whose cyclic modules are [Formula: see text]-modules. The motivation is the observation that a ring [Formula: see text] is semisimple artinian if and only if every [Formula: see text] -generated right [Formula: see text]-module is a [Formula: see text]-module. Many basic properties are obtained for the rings whose cyclics are [Formula: see text]-modules, and some structure theorems are proved. For instance, it is proved that a semiperfect ring has all cyclics [Formula: see text]-modules if and only if it is a direct product of a semisimple artinian ring and finitely many local rings, and that a right self-injective regular ring has all cyclics [Formula: see text]-modules if and only if it is a direct product of a semisimple artinian ring, a strongly regular ring and a [Formula: see text] matrix ring over a strongly regular ring. Applications to the rings whose [Formula: see text]-generated modules are [Formula: see text] -modules, and the rings whose cyclics are ADS or quasi-continuous are addressed.

scholarly journals Prime and special ideals in structural matrix rings over a ring without unity

1988 ◽  
Vol 45 (2) ◽  
pp. 220-226 ◽  
Author(s):  
L. Van Wyk
Keyword(s):  
Special Class ◽  
Associative Ring ◽  
Matrix Ring ◽  
Boolean Matrix ◽  
Prime Ideals ◽  
Matrix Rings ◽  
Quasi Order ◽  
Structural Matrix Ring ◽  
Complete Matrix ◽  
Structural Matrix

AbstractA. D. Sands showed that there is a 1–1 correspondence between the prime ideals of an arbitraty associative ring R and the complete matrix ring Mn(R) via P→ Mn(P). A structural matrix ring M(B, R) is the ring of all n × n matrices over R with 0 in the positions where the n × n boolean matrix B, B a quasi-order, has 0. The author characterized the special ideals of M(B, R′), in case R′ has unity, for certain special lasses of rings. In this note results of sands and the author are generalized to structural matrix rings over rings without unity. I t turns out that, although the class of prime simple rings is not a special class, Nagata's M-radical has the same form in structural matrix rings as the special radicals studied by the author.

scholarly journals A note on rings with the summand sum property

2015 ◽  
Vol 52 (4) ◽  
pp. 450-456
Author(s):  
Shen Liang
Keyword(s):  
Direct Summand ◽  
Regular Ring ◽  
Matrix Ring ◽  
Natural Numbers ◽  
Von Neumann Regular Ring ◽  
Von Neumann ◽  
Finite Matrix ◽  
Von Neumann Regular ◽  
Semisimple Ring

A ring R is called right SSP (SIP) if the sum (intersection) of any two direct summands of RR is also a direct summand. Left SSP (SIP) rings are defined similarly. There are several interesting results on rings with SSP. For example, R is right SSP if and only if R is left SSP, and R is a von Neumann regular ring if and only if Mn(R) is SSP for some n > 1. It is shown that R is a semisimple ring if and only if the column finite matrix ring ℂFMℕ(R) is SSP, where ℕ is the set of natural numbers. Some known results are proved in an easy way through idempotents of rings. Moreover, some new results on SSP rings are given.

Analysis of Lattice Single Layer Cylindrical Structures

1987 ◽  
Vol 2 (2) ◽  
pp. 87-91 ◽  
Author(s):  
Istvan HegedüS
Keyword(s):  
Stress Distribution ◽  
Matrix Method ◽  
Regular Ring ◽  
Lattice Structure ◽  
Single Layer ◽  
Cylindrical Structures ◽  
Lattice Construction

A matrix method is presented for the calculation of bar forces in a single layer lattice cylinder composed of regular ring polygons and symmetrically arranged bracing bars. Substantial differences occur between the stress distribution in the lattice structure and that of the membrane cylinder under the same load. Therefore, a membrane cylinder cannot be considered as a replacement continuum for the lattice construction. The purpose of the paper is to draw attention to the danger in the utilisation, without due caution, of this analogy.

Wear Model for Piston Ring and Cylinder Bore System

2005 ◽  
Author(s):  
Yunchao Qiu ◽  
Qian Zou ◽  
Gary C. Barber ◽  
Harold E. McCormick ◽  
Dequan Zou ◽  
...  
Keyword(s):  
Piston Ring ◽  
Thickness Distribution ◽  
Matrix Ring ◽  
Experimental Investigations ◽  
General Tendency ◽  
Wear Model ◽  
Wear Process ◽  
The Matrix ◽  
Surface Profiles ◽  
Cylinder Bore

A new wear model for piston ring and cylinder bore system has been developed to predict wear process with high accuracy and efficiency. It will save time and cost compared with experimental investigations. Surfaces of ring and bore were divided into small domains and assigned to corresponding elements in two-dimensional matrix. Fast Fourier Transform (FFT) and Conjugate Gradient Method (CGM) were applied to obtain pressure distribution on the computing domain. The pressure and film thickness distribution were provided by a previously developed ring/bore lubrication module. By changing the wear coefficients of the ring and bore with accumulated cycles, wear was calculated point by point in the matrix. Ring and bore surface profiles were modified when wear occurred. The results of ring and bore wear after 1 cycle, 10 cycles and 2 hours at 3600 rpm were calculated. They coincided well with the general tendency of wear in a ring and bore system.

scholarly journals RINGS OF DEFINABLE SCALARS OF VERMA MODULES

2007 ◽  
Vol 06 (05) ◽  
pp. 779-787 ◽  
Author(s):  
SONIA L'INNOCENTE ◽  
MIKE PREST
Keyword(s):  
Lie Algebra ◽  
Model Theory ◽  
Regular Ring ◽  
Verma Module ◽  
Closed Field ◽  
Verma Modules ◽  
Von Neumann Regular Ring ◽  
Von Neumann ◽  
Canonical Map ◽  
Von Neumann Regular

Let M be a Verma module over the Lie algebra, sl 2(k), of trace zero 2 × 2 matrices over the algebraically closed field k. We show that the ring, RM, of definable scalars of M is a von Neumann regular ring and that the canonical map from U( sl 2(k)) to RM is an epimorphism of rings. We also describe the Ziegler closure of M. The proofs make use of ideas from the model theory of modules.

CPU AND GPU PERFORMANCE ANALYSIS ON 2D MATRIX OPERATION

2021 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Kwek Benny Kurniawan ◽  
YB Dwi Setianto
Keyword(s):  
Graphic Processing Unit ◽  
Computing Time ◽  
General Purpose ◽  
Parallel Processors ◽  
Processing Unit ◽  
Matrix Operation ◽  
Industry Standard ◽  
Programming Interfaces ◽  
Complete Matrix ◽  
Matrix Calculation

GPU or Graphic Processing Unit can be used on many platforms in general GPUs are used for rendering graphics but now GPUs are general purpose parallel processors with support for easily accessible programming interfaces and industry standard languages such as C, Python and Fortran. In this study, the authors will compare CPU and GPU for completing some matrix calculation. To compare between CPU and GPU, the authors have done some testing to observe the use of Processing Unit, memory and computing time to complete matrix calculations by changing matrix sizes and dimensions. The results of tests that have been done shows asynchronous GPU is faster than sequential. Furthermore, thread for GPU needs to be adjusted to achieve efficiency in GPU load.

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