J-clean and Strongly J-clean Rings

Let R be a ring and J（R） the Jacobson radical. An element a of R is called（strongly） J-clean if there is an idempotent e ∈ R and w ∈ J（R） such that a = e ＋ w（and ew = we）. The ring R is called a（strongly） J-clean ring provided that every one of its elements is（strongly） J-clean. We discuss, in the present paper,some properties of J-clean rings and strongly J-clean rings. Moreover, we investigate J-cleanness and strongly J-cleanness of generalized matrix rings. Some known results are also extended.

Extensions of strongly π-regular general rings

The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.

Uniquely strongly clean triangular matrix rings

An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.

On Strongly Regular Rings

In this paper we investigate strongly regular rings. In terms of W-ideals of rings some characterizations of strongly regular rings are given.

ON STRONGLY REGULAR RINGS

?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.

Strongly s-Reflexive Rings Relative to a Monoid

For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring Q, we prove that R is strongly M-α-reflexive if and only if Q is strongly M-α-reflexive, where R is α-rigid, α is an epimorphism of R. The relationship between some special subrings of upper triangular matrix rings and strongly M-α-reflexive rings is also investigated. Several known results similar to strongly M-α-reversible rings are obtained.

Extensions of Morphic Rings

A ring R is called left morphic, if for any a ∈ R, there exists b ∈ R such that lR（a） =Rb and lR（b）= Ra. In this paper, we use the method which is different from that of Lee and Zhou to investigate when R[x, σ]/（x^n） is （left） morphic and when the ideal extension E（R, V） is （left） morphic. It is mainly shown that： （1） If is an automorphism of a division ring R, then S = R[x, σ]/（x^n） （n 〉 1） is a special ring. （2） If d,m are positive integers and n = dm, then E（Zn, mZn） is a morphic ring if and only if gcd（d, m） = 1.

When Exchange Rings are Von Neumann Regular

We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.

I-semi-π-regular Rings

Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.

Strongly Clean Matrix Rings over a Skew Monoid Ring

Let R be a ring with an endomorphismσ,F∪{0}the free monoid generated by U={u1,…,ut}with 0 added,and M a factor of F obtained by setting certain monomials in F to 0 such that M^(n)=0 for some n.Then we can form the non-semiprime skew monoid ring R[M;σ].A local ring R is called bleached if for any j∈J(R)and any u∈U(R),the abelian group endomorphisms l_(u)−r_(j) and l_(j)−r_(u) of R are surjective.Using R[M;σ],we provide various classes of both bleached and non-bleached local rings.One of the main problems concerning strongly clean rings is to characterize the rings R for which the matrix ring M_(n)(R)is strongly clean.We investigate the strong cleanness of the full matrix rings over the skew monoid ring R[M;σ].

On minimal quasi-injective modules and strong Kasch modules

设R为一个环，M为一个右R-模．若每个从M的单子模到M的同态都可以开拓为M的自同态，则称M为一个极小拟内射模．若每个单的右R-模都可以嵌入M，则称M为一个强Kasch模．本文研究了这两类模的一些刻画和性质．

基于激光拍频的高温传感技术研究

为实现强电磁及其他特殊高温环境的直接温度测量,提出并演示了一种新颖、简单、低成本的光纤高温温度检测系统,该系统利用法布里—珀罗激光二极管(FP-LD)的强反馈来实时检测反射光纤的温度。传感系统由通信用激光光源——FP-LD、光纤环镜Sagnac和光电探测器(PD)组成。利用该系统实现了温度变化范围为105~1025℃的高温温度传感。实验结果表明,在光纤软化温度内其强反馈拍频信号(BFS)的频率偏移与温度变化呈线性关系,可广泛应用于冶金、航空航天等领域的高温检测。

NGR-clean环

若环R中的任意元素都能表示成一个(强)π-正则元和一个幂零元之和,则称环R是(强)NGR-clean环。研究给出(强)NGR-clean环的一些基本性质,证明了若I是环R的诣零理想,则R是NGR-clean环当且仅当R/I是NGR-clean环。此外,还研究了(强)NGR-clean环与一些环类之间的联系以及(强)NGR-clean环的几类扩张。

立达G32型环锭细纱机控制系统改造

针对立达G32型环锭细纱机在运行中出现纱线强捻、电气元件老化、系统兼容性差等问题,介绍其CPU、操作面板、驱动器等控制系统以及电控箱电气元件升级换代的具体操作,并对比验证改造前后的技术要求和改造效果。指出:改造后的立达G32型环锭细纱机控制系统稳定可靠、兼容性较高,能保持原车布局结构且操作维修方便;改造成本低,整车性能良好,生产纱线的各项指标合格。

A Generalization of Strongly Nil Clean Rings

Generalizing the notion of strongly nil clean rings,we introduce strongly quasinil clean rings.Some fundamental properties and equivalent characterizations of this class of rings are provided.By means of g-Drazin inverses,Cline's formula and Jacobson's lemma for strongly quasi-nil clean elements are investigated.

Paterns and regularity of ring distribution of seismic activity before great earthquakes in China

A systematic study on ″ring phenomena″ frequently occurring before great earthquakes has made in this paper, which has analyzed the features of ring distributions before 16 great earthquakes and part of large earthquakes in China and its boundary areas, and discussed their features of generality, regularity and predictive meaning. The results have showed that moderate earthquakes or larger earthquakes distribute around the epicenter like a ring from decades to hundred years before the great earthquakes of magnitude more than 7, which is a general phenomenon of great earthquakes without an exception. The active ring generally occurs in the areas from hundreds to thousands of kilometers from the epicenter(according to the magnitude). The seismicity in the ring has three basic stages with different features. in the first stage, seismicity remains at low level and the earthquakes distribute scatteredly, while the source area of the future great earthquake remains quiet; in the second stage, the seismicity strengthens, whose frequency, intensity, concentrated degree, released rate of strain and ratio of distributed area etc. increase, while the quiet area decreases or disappears; in the third stage, the seismicity is weaker than in the former stage, and the quiet area appears again. The source area surrounded by the active ring might have three periods of activity(called as early term, medium term and late term foreshocks activity). The length of the quiet area undergoes the process from large to small, then to large. Therefore, we can estimate the occurring place, magnitude and seismogenic stage of great earthquake according to the area,length and the seismicity in the active ring, which is valuable to make a long term prediction of great earthquakes. At last, we had a preliminary discussion on the mechanism of active ring formation.

具有强扰动程度的振动局域化现象研究

振动局域化效应是非周期结构的典型特征,而扰动程度是衡量结构非周期性的重要指标。为研究强扰动程度对振动传递特性影响的一般规律,首先以弹簧振子系统为例,采用模态分析法和基于统计理论的波传递法计算强局域化系数。同时基于通频带近似的等效方法,将一维系统的结论应用到二维结构,推导出非周期环肋圆柱壳的强局域化系数。研究结果实现了强扰动程度下振动局域化系数的定量计算,所得结论可为通过增加扰动程度而降低结构的振动传递性能提供理论支撑。

Strong Skew Commutativity Preserving Maps on Rings with Involution

Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф： R →R is strong skew commutativity preserving （that is, satisfies Ф（A）Ф（B） - Ф（B）Ф（A）＊ ： AB- BA＊ for all A, B ∈R） if and only if there exist a map f ： R → ZSz（R） and an element Z ∈ ZS（R） with Z^2 =I such that Ф（A） =ZA ＋ f（A） for all A ∈ R, where ZS（R） is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime ＊-rings and von Neumann algebras with no central summands of type I1 are characterized.

Strong Commutativity-preserving Generalized Derivations on Semiprime Rings

Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered.

Notes on Rings with Strong 2-Sum Property

A ring is said to satisfy the strong 2-sum property if every element is a sum of two commuting units.In this note,we present some sufficient or necessary conditions for the matrix ring over a commutative local ring to have the strong 2-sum property.