The existence of clean element and feebly clean element in a matrix ring

2020 ◽  
Author(s):  
Ida Fitriana Ambarsari ◽  
Santi Irawati ◽  
I. Made Sulandra ◽  
Hery Susanto ◽  
Angelina Chin Yan Mui ◽  
...  
Keyword(s):  
Matrix Ring ◽  
Clean Element

A nil-clean 2 × 2 matrix over the integers which is not clean

2014 ◽  
Vol 13 (06) ◽  
pp. 1450009 ◽  
Author(s):  
Dorin Andrica ◽  
Grigore Călugăreanu
Keyword(s):  
Matrix Ring ◽  
Clean Ring ◽  
The Matrix ◽  
Nil Clean Ring ◽  
Clean Element

While any nil-clean ring is clean, the last eight years, it was not known whether nil-clean elements in a ring are clean. We give an example of nil-clean element in the matrix ring ℳ2(Z) which is not clean.

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.

Semiprime Goldie Generalised Matrix Rings

1995 ◽  
Vol 38 (2) ◽  
pp. 174-176 ◽  
Author(s):  
Michael V. Clase
Keyword(s):  
Matrix Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Rings ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions are given for a generalised matrix ring to be semiprime right Goldie.

Artinian Modules Over a Matrix Ring

2000 ◽  
pp. 101-105 ◽  
Author(s):  
K. I. Pimenov ◽  
A. V. Yakovlev
Keyword(s):  
Matrix Ring ◽  
Artinian Modules

scholarly journals Carbonitration of a Tool for Pressing Stainless Steel Pipes

2020 ◽  
Vol 7 (2) ◽  
pp. C17-C21
Author(s):  
I. V. Ivanov ◽  
M. V. Mohylenets ◽  
K. A. Dumenko ◽  
L. Kryvchyk ◽  
T. S. Khokhlova ◽  
...  
Keyword(s):  
Heat Treatment ◽  
Thermal Treatment ◽  
Heat Resistance ◽  
Alkali Metals ◽  
Matrix Ring ◽  
High Hardness ◽  
Operating Conditions ◽  
Matrix Rings ◽  
Conventional Heat Treatment ◽  
The Stability

To upgrade the operational stability of the tool at LLC “Karbaz”, Sumy, Ukraine, carbonation of tools and samples for research in melts of salts of cyanates and carbonates of alkali metals at 570–580 °C was carried out to obtain a layer thickness of 0.15–0.25 mm and a hardness of 1000–1150 НV. Tests of the tool in real operating conditions were carried out at the press station at LLC “VO Oscar”, Dnipro, Ukraine. The purpose of the test is to evaluate the feasibility of carbonitriding of thermo-strengthened matrix rings and needle-mandrels to improve their stability, hardness, heat resistance, and endurance. If the stability of matrix rings after conventional heat setting varies around 4–6 presses, the rings additionally subjected to chemical-thermal treatment (carbonitration) demonstrated the stability of 7–9 presses due to higher hardness, heat resistance, the formation of a special structure on the surface due to carbonitration in salt melts cyanates and carbonates. Nitrogen and carbon present in the carbonitrided layer slowed down the processes of transformation of solid solutions and coagulation of carbonitride phases. The high hardness of the carbonitrified layer is maintained up to temperatures above 650 °C. If the stability of the needle-mandrels after conventional heat treatment varies between 50–80 presses, the needles, additionally subjected to chemical-thermal treatment (carbonitration) showed the stability of 100–130 presses due to higher hardness, wear resistance, heat resistance, the formation of a special surface structure due to carbonitration in melts of salts of cyanates and carbonates. Keywords: needle-mandrel, matrix ring, pressing, heat treatment, carbonitration.

scholarly journals Rings in which every element is either a sum or a difference of a nilpotent and an idempotent

2016 ◽  
Vol 15 (08) ◽  
pp. 1650148 ◽  
Author(s):  
Simion Breaz ◽  
Peter Danchev ◽  
Yiqiang Zhou
Keyword(s):  
Division Ring ◽  
Matrix Ring ◽  
Decomposition Theorem ◽  
Arbitrary Ring ◽  
Clean Rings ◽  
Clean Ring ◽  
Unital Rings ◽  
Nil Clean Ring ◽  
Comprehensive Study

Generalizing the notion of nil-cleanness from [A. J. Diesl, Nil clean rings, J. Algebra 383 (2013) 197–211], in parallel to [P. V. Danchev and W. Wm. McGovern, Commutative weakly nil clean unital rings, J. Algebra 425 (2015) 410–422], we define the concept of weak nil-cleanness for an arbitrary ring. Its comprehensive study in different ways is provided as well. A decomposition theorem of a weakly nil-clean ring is obtained. It is completely characterized when an abelian ring is weakly nil-clean. It is also completely determined when a matrix ring over a division ring is weakly nil-clean.

scholarly journals Complementation of the Jacobson group in a matrix ring

2005 ◽  
Vol 72 (2) ◽  
pp. 317-324
Author(s):  
David Dolžan
Keyword(s):  
Normal Subgroup ◽  
Commutative Ring ◽  
Jacobson Radical ◽  
Matrix Ring ◽  
Graded Rings ◽  
Matrix Rings ◽  
Generators And Relations ◽  
Group Of Units ◽  
The Matrix ◽  
Finite Commutative Ring

The Jacobson group of a ring R (denoted by  = (R)) is the normal subgroup of the group of units of R (denoted by G(R)) obtained by adding 1 to the Jacobson radical of R (J(R)). Coleman and Easdown in 2000 showed that the Jacobson group is complemented in the group of units of any finite commutative ring and also in the group of units a n × n matrix ring over integers modulo ps, when n = 2 and p = 2, 3, but it is not complemented when p ≥ 5. In 2004 Wilcox showed that the answer is positive also for n = 3 and p = 2, and negative in all the remaining cases. In this paper we offer a different proof for Wilcox's results and also generalise the results to a matrix ring over an arbitrary finite commutative ring. We show this by studying the generators and relations that define a matrix ring over a field. We then proceed to examine the complementation of the Jacobson group in the matrix rings over graded rings and prove that complementation depends only on the 0-th grade.

Golden Matrix Ring Mod p

2008 ◽  
Vol 81 (3) ◽  
pp. 214-216
Author(s):  
Kung-Wei Yang
Keyword(s):  
Matrix Ring ◽  
Mod P

scholarly journals Strong Regularity in Arbitrary Rings

1952 ◽  
Vol 4 ◽  
pp. 51-53 ◽  
Author(s):  
Tetsuo Kandô
Keyword(s):  
Matrix Ring ◽  
Strong Regularity ◽  
Full Matrix ◽  
Regular Ideal ◽  
Strongly Regular ◽  
Full Matrix Ring

An element a of a ring R is called regular, if there exists an element x of R such that a×a = a, and a two-sided ideal a in R is said to be regular if each of its elements is regular B. Brown and N. H. McCoy [1] has recently proved that every ring R has a unique maximal regular two-sided ideal M(R), and that M(R) has the following radical-like property: (i) M(R/M(R)) = 0; (ii) if a is a two-sided ideal of R, then M(a) = a ∩ M(R); (iii) M(Rn) = (M(R))n, where Rn denotes a full matrix ring of order n over R. Arens and Kaplansky [2] has defined an element a of R to be strongly regular when there exists an element x of R such that a2x = a. We shall prove in this note that replacing “regularity” by “strong regularity,” we have also a unique maximal strongly regular ideal N(R), and shall investigate some of its properties.

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